幾何
三角形、圓、解析幾何與證明題。
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triangle nop is formed by connecting the midpoints of the side of trian…
\(16\)
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4 what is the measurement of the angle? choose the best estimate. 45° 1…
\(90^{\circ}\)
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12 what is the measurement of the angle? choose the best estimate. angl…
\(91^{\circ}-179^{\circ}\)
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9 which pair of line segments appears to be perpendicular?
$\overline{CD}$ and $\overline{BC}$
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5. here is a polygon on a grid. a. draw a scaled copy of the polygon us…
a. and b. (Drawings are done by scaling coordinates as described above). c. Yes, Polygon A is a scaled copy of Polygon B. The scale factor is \(6\)
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2. the segment xy with endpoints x(3, 1) and y(2, -2) is rotated such t…
The rotation is \(180^{\circ}\) about the origin. The algebraic representation is \((x,y)\to(-x,-y)\)
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you do: check for understanding point q with coordinates (4, -7) is rot…
The rotation is a \(90^{\circ}\) counter - clockwise rotation about the origin. The algebraic representation is \((x,y)\to(-y,x)\)
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you do check for understanding point q with coordinates (4, -7) is rota…
The rotation is a \(90^{\circ}\) counter - clockwise rotation about the origin. The algebraic rule is \((x,y)\to(-y,x)\)
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classify the angle pair as corresponding, alternate interior, alternate…
1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles 4. Corresponding angles 5. Corresponding angles 6. Consecutive interior angles
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use the given information to decide if ( aparallel b,mparallel l ), or …
a. $a\parallel b$, Corresponding Angles Postulate b. $a\parallel b$, Alternate Interior Angles Theorem c. Neither d. $l\parallel m$, Same - Side Interior Angles Theorem e. Neither…
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solve the inequality and graph the solution on the line -2x - 5 ≥ -21 a…
Inequality Notation: \(x\leq8\) For the number line: Place a closed - circle at \(8\) (because the inequality is \(\leq\)) and shade to the left of \(8\) (since \(x\) is less than…
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solve the inequality and graph the solution on the line pre -8 - 4x > -…
Inequality Notation: \(x < 2\) For the number line: Draw an open circle at \(2\) (since \(x\) is not equal to \(2\)) and shade the line to the left of \(2\) (because \(x\) is less…
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solve the inequality and graph the solution on the line -2 + 7x ≤ -16 a…
Inequality Notation: \(x\leq - 2\) For the number - line: Place a closed circle at \(-2\) (since the inequality is \(\leq\)) and shade to the left of \(-2\) (because \(x\) is less…
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solve the inequality and graph the solution on the line provided. 4x - …
Inequality Notation: \(x>-6\) To graph on the number line: Place an open circle at \(-6\) (because the inequality is \(>\), not \(\geq\)) and draw an arrow to the right.
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solve the inequality and graph the solution on the line provided. 8 - 4…
Inequality Notation: \(x < 3\) For the number - line: Place an open circle at \(x = 3\) (because \(x\) is not equal to 3) and shade the line to the left of 3 (towards the negative…
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a1 marquer un point a sur votre feuille. combien de droites pouvez-vous…
- La droite \( m \) est \( (AE) \). - La droite \( n \) est \( (BC) \). - La droite \( p \) est \( (AB) \).
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find the measure of \\( \\angle k l n \\). after you enter your answer …
\(100\)
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the image of the point (8,1) under a translation is (9,2). find the coo…
\((6,6)\)
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question what is the image of the point (1,3) after a rotation of 270° …
\((3,-1)\)
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question what is the image of the point (9,8) after a rotation of 180° …
\((-9,-8)\)
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22. when a line parallel to one side of a triangle divides the other tw…
22. d. AA Criterion 23. d. Dilation and translation 24. c. 4.8 (Note: There was a miscalculation in the options provided, but using the formula \(QS=\frac{PQ\times QR}{PR}\), with…
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15. what is the length of the hypotenuse of a right triangle with legs …
d. 25 units
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11. what is the length of the hypotenuse of a right triangle with legs …
B. 25 units
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15. what is the length of the hypotenuse of a right triangle with legs …
d 25 units
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15. what is the length of the hypotenuse of a right triangle with legs …
a. 25 units
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8. two concentric circles share the same center but have radii of 3.5 a…
7. a. 2 9. d. \((1.5,0)\) 10. c. \((3,1.5)\) 11. b. 2 12. d. Dilation and translation 13. b. \((8,8)\) 14. b. 32 meters
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1. in a diagram, △abc has angles 50°, 60°, and 70°. if △def has the sam…
a. The triangles are similar. # 2.
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15. use the vertical line test to determine if each relation is a funct…
The relation (the circle) is not a function.
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in the triangle, suppose that ( mangle q=(x + 3)^{circ}, mangle r=(2x +…
(a) Equation: \((x + 3)+(2x + 7)+7x=180\) (b) \(m\angle Q = 20^{\circ}\), \(m\angle R = 41^{\circ}\), \(m\angle S = 119^{\circ}\)
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in the triangle, suppose that ( mangle h=(4x - 9)^{circ}, mangle i=(3x …
(a) Equation: \(8x-12 = 180\) (b) \(m\angle H = 87^{\circ}\), \(m\angle I=69^{\circ}\), \(m\angle J = 24^{\circ}\)
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2 - 56. for each triangle below, solve for the variable and answer the …
a. \(x = 45^{\circ}\), \(\triangle ABC\) is a right - isosceles triangle. b. \(y = 154^{\circ}\), the triangle is an isosceles triangle.
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8. given \\( \\triangle m t w \\cong \\triangle b g k \\), find the val…
\(x = 12\) and \(y = 8\)
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2 - 53. the area of the triangle at right is 25 square feet. determine …
The value of \( h = 10\) feet. The perimeter of the triangle is approximately \( 22.66\) feet.
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5. in this figure, \\( \\overline { p q } \\parallel \\overline { l n }…
C. 6
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4. look at the figure below. name one additional piece of information t…
One additional piece of information could be \(\frac{yz}{st}=\frac{1}{3}\) (or \(\angle z=\angle t\) or \(\frac{xz}{rt}=\frac{1}{3}\))
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3. in this figure, triangle lmn is similar to triangle pqr. complete th…
\(\frac{MN}{LM}=\frac{QR}{PQ}\)
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answer the questions below. (a) the area of a rectangular field is 5576…
(a) \(68\space m\) (b) \(71\space cm\)
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answer the questions below. (a) the perimeter of a rectangular garden i…
(a) \(l=171 - 75=96\) m. (b) \(w=\frac{6351}{87}=73\) cm.
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6. the hypotenuse of a right isosceles triangle is 5 cm long. a) write …
a) The base \(b = 5\sin45^{\circ}\) and height \(h = 5\cos45^{\circ}\) (or \(b = h=\frac{5\sqrt{2}}{2}\) cm) b) The area of the triangle is \(\frac{25}{4}\text{ cm}^2\)
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cumulative review define a - b - c (b is between a and c) as follows. 1…
\(CP = 115\) inches and \(PD = 37\) inches.
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write an algebraic expression for each quantity. 2.7 43. the second ang…
43. The algebraic expression for the second angle of the linear pair is \(180 - x\). 44. The algebraic expression for the complement of the angle \((x + 23)^{\circ}\) is \(67 - x\…
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answer the questions below. (a) the area of a rectangular field is 6138…
(a) \(93\space m\) (b) \(83\space cm\)
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which lines can be proved to be parallel from each given statement? nam…
8. \(a\parallel b\), Corresponding Angles Postulate 9. \(c\parallel d\), Alternate Exterior Angles Theorem 10. \(a\parallel b\), Alternate Interior Angles Theorem 11. None 12. \(c…
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answer the questions below. (a) the perimeter of a rectangular garden i…
(a) \(99\) m (b) \(56\) cm
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supply the missing statements and reasons in the following two - column…
| Statements | Reasons | |--|--| | 1. \(\overline{CB}\cong\overline{YZ}\) | 1. given | | 2. \(CB = YZ\) | 2. definition of congruent segments | | 3. \(CB + BY=YZ + BY\) | 3. Addit…
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16. name the definition, postulate, theorem, or property justifying eac…
a. Vertical Angles Theorem b. Definition of supplementary angles c. Definition of congruent angles d. Transitive Property of Congruence e. Angle - Addition Postulate
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15. complete each statement that is justified by the given reason. a. i…
a. \(PQ = RS\) b. supplementary c. \(XM = MY\) (or \(XM=\frac{1}{2}XY\) and \(MY=\frac{1}{2}XY\)) d. \(U\) is between \(T\) and \(V\)
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4. apply casey builds the gate shown, with two solid triangular panels.…
Yes, the solid panels are congruent. Using the AAS (Angle - Angle - Side) congruence criterion, each triangle has a \(90^{\circ}\) angle, a \(38^{\circ}\) angle, and the side oppo…
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11. find ( mangle deg ) and ( mangle def ). a. ( mangle deg ) b. ( mang…
a. \(m\angle DEG = 60^{\circ}\) b. \(m\angle DEF=144^{\circ}\)
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11. find ( mangle deg ) and ( mangle def ). a. ( mangle deg ) b. ( mang…
For problem 11 (assuming \(x = 9\)): a. \(m\angle DEG = 68^{\circ}\) b. \(m\angle DEF=166^{\circ}\) For problem 12: a. \(LM = 132\) b. \(LN = 264\)
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the length of a rectangle is 3 yd longer than its width. if the perimet…
length: \( 15 \) yd, width: \( 12 \) yd
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the length of a rectangle is four times its width. if the perimeter of …
length: \( 40 \) cm, width: \( 10 \) cm
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9. find each angle measure. a. ( mangle apb ) b. ( mangle cpe ) c. ( ma…
a. \(90^{\circ}\) b. \(57^{\circ}\) c. \(68^{\circ}\) d. \(22^{\circ}\) e. \(145^{\circ}\)
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8) in \\( \\triangle a b c, \\angle a = 58 ^ { \\circ }, a c = 22 \\), …
\(\angle B\approx48.3^{\circ}\), \(\angle C\approx73.7^{\circ}\), \(AB\approx28.3\)
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find the coordinate of p if q is the midpoint of \\( \\overline { p r }…
\(p = 243\)
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2. given: \\( \\angle p \\cong \\angle s, \\overline{tq} \\cong \\overl…
1. \(\angle P\cong\angle S,\overline{TQ}\cong\overline{RQ}\) 2. Vertical Angles Theorem 3. \(\triangle QRS\cong\triangle QTP\)
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2. given: \\( \\angle p \\cong \\angle s, \\overline{tq} \\cong \\overl…
1. \(\angle P\cong\angle S,\overline{TQ}\cong\overline{RQ}\) 2. Vertical Angles Theorem 3. \(\triangle QRS\cong\triangle QTP\)
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7. apply will the folded flag fit in the shadow box shown? explain. fla…
Yes, the folded flag will fit in the shadow box. Because the two triangles (the folded flag and the shadow - box space) are congruent by the SAS (Side - Angle - Side) congruence c…
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erin and frannie entered a rug design contest. the rules stated that th…
Design 1: Areas of sections \(450\), \(450\), \(540\) square inches; total area \(1440\) square inches. Design 2: Areas of sections \(480\), \(480\), \(480\) square inches; total …
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are the triangles below acute, obtuse, or right? triangle a triangle b …
Triangle A: Acute, Triangle B: Right, Triangle C: Obtuse, Triangle D: Right
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are the triangles below acute,obtuse, or right? triangle a triangle b t…
Triangle A: Right, Triangle B: Acute, Triangle C: Right, Triangle D: Obtuse
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given: ( g parallel h ) and ( angle 2 cong angle 3 ) prove: ( e paralle…
converse corresponding angles theorem
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are the triangles below acute, obtuse, or right? triangle a triangle b …
Triangle A: Acute; Triangle B: Obtuse; Triangle C: Acute; Triangle D: Right - angled.
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a rectangle has a length of 18 cm and a width of 4 cm. what is its peri…
\(44\) cm
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ng lines parallel in the diagram, ( g parallel h ), ( mangle1=(4x + 36)…
\(120^{\circ}\)
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v. geometry sem a geometry ng lines parallel what must be the value of …
\(20\)
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given: ( overline{ab} parallel overline{dc} ) and ( mangle2 = mangle4 )…
\(m\angle1 + m\angle4 = 180^{\circ}\)
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6. which of the following diagrams represent the alternate interior ang…
The fourth diagram (with ∠2 and ∠6) represents the Alternate Interior Angles Theorem and its Converse.
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5. complete the proof. given: ( wx = xy ), ( vx = xz ) prove: ( angle w…
| Statements | Reasons | |---|---| | 1. \(WX = XY\), \(VX = XZ\) | 1. Given | | 2. \(\angle VXW=\angle YXZ\) | 2. Vertical Angles Theorem | | 3. \(\triangle VXW\cong\triangle YXZ\…
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geometry sem a geometry lines parallel two lines, a and b, are crossed …
\(55+125 = 180\)
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5. which of the following diagrams represent the consecutive interior a…
The fourth option (the one with angles \(3\) and \(5\) where if \(\angle3\) and \(\angle5\) are supplementary, then \(j\parallel k\))
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3. the diagram best represents which of the following theorems parallel…
If \(l\parallel m\) and \(m\parallel n\), then \(l\parallel n\)
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parallel lines and their angles: theorems (p→q) and their converse (q→p…
Corresponding Angles Theorem, Consecutive Interior Angles Theorem, Alternate Exterior Angles Theorem, Alternate Interior Angles Theorem
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4 - 3 additional practice proving and applying the sas and sss congruen…
1. Congruent by SAS 2. Congruent by SAS 3. Not enough information 4. Congruent by SSS
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parallel lines and their angles: theorems (p→q) and their converse (q→p…
\(q ightarrow p\)
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which of the following statements is true for similar triangles? a. onl…
c. Corresponding angles are congruent and sides are proportional
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in △abc and △def, ∠a = 60°, ∠d = 60°, ab = 6, ac = 9, and de = 3. find …
b. \(4.5\mathrm{cm}\)
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if ∠a = ∠d = 80°, ab = 16 cm, ac = 24 cm, and de = 8 cm, what is the va…
d. \(12\mathrm{cm}\)
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what is the purpose of the sas similarity criterion? a. to identify sup…
d. To prove the similarity of two triangles
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ing lines parallel given: ( mparallel n ) and ( mangle2 + mangle3 = 180…
2. \(\angle1\cong\angle2\) (so the number in the first box is \(2\)) 4. \(m\angle1 + m\angle3=180^{\circ}\) (so the numbers in the second and third boxes are \(1\) and \(3\) respe…
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in △ghi and △jkl, if ∠g≅∠j, gh = 10, gi = 15, and jk = 5, what is the m…
a. \(7.5\mathrm{cm}\)
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which of the following situations does not use the sas similarity crite…
For the first question: B. Proving congruence of two triangles For the second question: D. Triangles \(PQR\) and \(STU\) are similar by SAS similarity
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ritas backyard has cement and grass. find the area of the part with cem…
\(20\)
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4520va v. geometry sem a proving lines parallel which lines are paralle…
Lines \(a\) and \(b\) are parallel because their corresponding angles are congruent.
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given △xyz∼△pqr, if ∠x=70°, ∠p=70°, and the sides xy/xz = pq/pr = 2, wh…
B. The triangles are similar with a scale factor of 2
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ng lines parallel parallel lines c and f are cut by transversal b what …
\(130\)
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which of the following is an example of a correct proportion for simila…
A. \(AB/DE = AC/DF\)
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which of the following ratios would indicate that triangles are similar…
a. \(6/3 = 9/4.5\)
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27. if ∠a = 50° & ∠e = 70°, what is the measure of... ∠b = ∠c = ∠d = ∠f…
\(\angle b = 40^{\circ}\), \(\angle c = 70^{\circ}\), \(\angle d = 110^{\circ}\), \(\angle f = 70^{\circ}\), \(\angle g = 110^{\circ}\), \(\angle h = 40^{\circ}\)
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ving lines parallel given the information in the diagram, which theorem…
converse alternate exterior angles theorem
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26. remember: the 2 arrow heads on the two lines signifies that those l…
\(90^{\circ}\)
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each graph, decide if the two lines are parallel, perpendicular, or nei…
Graph 1: Parallel; Graph 2: Perpendicular; Graph 3: Neither; Graph 4: Neither
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parallel lines e and f are cut by transversal b. what is the value of x…
\(25\)
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24. if one of the exterior angles of a pair of parallel lines cut by a …
B. 75 degrees
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23. two parallel lines cut by a transversal form corresponding angles o…
Congruent angles
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22. what is the sum of the measures of two supplementary angles? 90 deg…
180 degrees
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21. when two lines are cut by a transversal so that corresponding angle…
The lines are parallel
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20. if alternate interior angles formed by parallel lines and a transve…
35 degrees
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19. two parallel lines are intersected by a transversal forming alterna…
85 degrees
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18. if two parallel lines are intersected by a transversal, what can yo…
They are congruent