Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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read the sentence. the squirrel who ran in circles around the circumfer…
The squirrel, who ran in circles around the circumference of the tree, chattered angrily at the curious cat.
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find the value of x.
\(x = 1\)
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translate the triangle 4 units right and 3 units down. what are the coo…
The coordinates of the image are \( L'(0,-2) \), \( K'(3,-2) \), \( J'(3,0) \).
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which of the following is not true for an isosceles trapezoid. the legs…
The diagonals are bisected (green option)
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what is the m∠r?
$75^{\circ}$
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what is the m∠s?
\(75^{\circ}\)
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cd is the midsegment of trapezoid abgf. ab = 7, fg = 11, cd =?
\( 9 \)
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solve the inequality and graph the solution. ( k + 6 geq 10 ) to draw a…
The solution of the inequality \(k + 6\geq10\) is \(k\geq4\). On the number - line, we have a closed circle at \(4\) and a ray extending to the right.
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if \\( \\triangle jkl \\) is isosceles, what is \\( m \\angle jkl \\)?
$106^{\circ}$
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solve the inequality and graph the solution. 3f > 6 to draw a ray, plot…
The solution of the inequality \(3f>6\) is \(f>2\). On the number - line, there is an open circle at \(2\) and an arrow pointing to the right.
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what is the name of this polygon? parallelogram rhombus trapezoid kite
Trapezoid
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cd is the midsegment of trapezoid abgf. ab = 17, fg = ?, cd = 32
\(FG = 47\)
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in a kite, the diagonals are ______________. congruent supplementary bi…
perpendicular
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solve the inequality and graph the solution. \\( \\frac { y } { 2 } < -…
The solution of the inequality is $y < - 4$. On the number - line, we plot an open circle at $-4$ and draw a ray to the left.
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move the points below to create a venn diagram that represent the sets …
Move \(V\) and \(VII\) to the overlapping region (intersection) of the two circles (representing \(A\) and \(B\)). Move \(I\), \(III\), \(VI\) to the non - overlapping part of the…
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what is the m∠c?
\(98^{\circ}\)
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solve the inequality and graph the solution. m - 19 < -17 to draw a ray…
The solution of the inequality is \(m<2\). On the number line, there is an open circle at \(2\) and a ray extending to the left.
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what is the m∠a?
\(98^{\circ}\)
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m<a = 108. what is m<c?
\(108\)
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solve the inequality and graph the solution. $v - 6 \\leq 2$ to draw a …
The solution of the inequality \(v - 6\leq2\) is \(v\leq8\). On the number - line, there is a closed circle at \(8\) and an arrow pointing to the left.
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solve the inequality and graph the solution. g + 2 > -2 to draw a ray, …
The solution is \(g > - 4\). On the number - line, there is an open circle at -4 and a ray extending to the right.
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solve the inequality and graph the solution. \\frac{k}{3} \\geq -1 to d…
The solution of the inequality is \(k\geq - 3\). On the number - line, we have a closed circle at \(-3\) and a ray extending to the right.
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what is m∠rts in the triangle below?
\(78^{\circ}\)
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solve the inequality and graph the solution. \\( \\frac { k } { 3 } \\g…
The solution of the inequality is \(k\geq - 3\). On the number - line, there is a closed circle at \(-3\) and a ray extending to the right.
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solve the inequality and graph the solution. \\( \\frac { y } { 3 } \\g…
The solution of the inequality is \(y\geq6\). On the number - line, we plot a closed circle at \(y = 6\) (because the inequality is \(\geq\), including the equal part) and draw an…
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what is the length of side jk?
\(33\)
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solve the inequality and graph the solution. $w + 1 leq 7$ to draw a ra…
The solution of the inequality is \( w\leq6 \). On the number - line, there is a closed circle at \( 6 \) and an arrow pointing to the left.
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what is the measure of ab?
\(12\)
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solve the inequality and graph the solution. 4f ≤ -8 to draw a ray, plo…
The solution of the inequality is \( f\leq - 2 \). On the number line, there is a closed circle at \( - 2 \) and an arrow pointing to the left.
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solve the inequality and graph the solution. 3r ≤ -6 to draw a ray, plo…
The solution of the inequality \(3r\leq - 6\) is \(r\leq - 2\). On the number - line, we have a closed circle at \(-2\) (because the inequality includes equality, i.e., \(r\) can …
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amaya is asked to find the side lengths of the triangle shown. what is …
The value of \(x\) is \(5\), the length of the top - left side is \(10\), and the length of the bottom - left side is \(10\).
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select the correct answer. a square - shaped canvas painting was enlarg…
A. 17 centimeters
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solve the inequality and graph the solution. b + 7 ≥ 10 to draw a ray, …
The solution of the inequality \(b + 7\geq10\) is \(b\geq3\). On the number line, we have a closed circle at \(3\) and a ray extending to the right.
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determine a series of transformations that would map polygon ( abcde ) …
A reflection over the \(x -\)axis followed by a translation \(12\) units to the left and \(7\) units up.
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solve the inequality and graph the solution. 2g > 8 to draw a ray, plot…
The solution of the inequality \(2g>8\) is \(g > 4\). On the number line, there is an open circle at \(4\) and a ray extending to the right.
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solve the inequality and graph the solution. c + 2 > 8 to draw a ray, p…
The solution of the inequality \(c + 2>8\) is \(c>6\). On the number - line, there is an open circle at \(6\) and an arrow pointing to the right.
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solve the inequality and graph the solution. 3c < 9 to draw a ray, plot…
The solution of the inequality \( 3c<9 \) is \( c < 3 \). On the number line, there is an open circle at \( 3 \) and a ray extending to the left.
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what is the measure of the highlighted arc? \\( \\overline { a c } \\) …
\(220^{\circ}\)
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solve the inequality and graph the solution. \\( \\frac { p } { 2 } \\g…
The solution of the inequality is \(p\geq6\). On the number line, there is a closed circle at \(6\) and an arrow pointing to the right.
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solve the inequality and graph the solution. 5g < 10 to draw a ray, plo…
The solution is \(g\lt2\). On the number - line, there is an open circle at \(2\) and an arrow pointing to the left.
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what is the measure of the highlighted arc? ab is a diameter. enter deg…
\(100\)
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problem 3 identifying parallelograms vehicle lifts a truck sits on the …
The maximum height that the vehicle lift can elevate the truck is \(6\) ft. This is because when the lift is at its maximum height, the non - base side (the arm) of the parallelog…
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find the volume of the rectangular prism.
\(125\)
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solve the inequality and graph the solution. 5q ≤ 10 to draw a ray, plo…
The solution of the inequality \( 5q\leq10 \) is \( q\leq2 \). On the number line, there is a closed circle at \( 2 \) and an arrow pointing to the left.
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select whether each statement is always true, sometimes true, or never …
1. Never true 2. Sometimes true 3. Always true
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the figure shows two parallel lines intersected by two transversals. tw…
\(120\)
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solve the inequality and graph the solution. \\( \\frac { b } { 2 } \\l…
The solution of the inequality is \(b\leq8\). On the number - line, there is a closed circle at \(8\) and a ray extending to the left.
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solve the inequality and graph the solution. v + 8 ≤ 9 to draw a ray, p…
The solution of the inequality is \(v\leq1\). On the number line, there is a closed circle at \(1\) and a ray extending to the left.
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the figure shows two parallel lines intersected by two transversals. tw…
\(63\)
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lines $\\overline{ac}$ and $\\overline{bd}$ are diagonals of $abcd$. wh…
\(x = 6\) (the first option)
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use the image to answer the question. given the rectangle abcd as shown…
\(1\)
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9. question: an angle measures x + 50. its supplement measures 2x - 20.…
A. \(x = 50\)
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got it? 1. use the diagram at the right. for what values of x and y mus…
\(x = 10\) and \(y=6\)
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the figure to the right shows two parallel lines intersected by a trans…
\(110\)
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if ( x = 67^{circ} ), find the measures of angles 1, 2, and 3. ( mangle…
\(m\angle3 = 113^{\circ}\)
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if ( x = 67^{circ} ), find the measures of angles 1, 2, and 3. ( mangle…
\(m\angle2 = 67^{\circ}\)
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this matrix represents the length and width of a rectangle: ( r=left\be…
\(a = 48\), \(b = 36\)
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13. question: angles a, b, and c form a straight line (they are supplem…
A. \(x = 20\) ### 14.
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if ( x = 67^{circ} ), find the measures of angles 1, 2, and 3. ( mangle…
\(m\angle1 = 113^{\circ}\), \(m\angle2=67^{\circ}\), \(m\angle3 = 113^{\circ}\)
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find the measure of the complement and the supplement of 8°. what is th…
\(172^{\circ}\)
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solve the inequality and graph the solution. ( k - 5 leq 2 ) to draw a …
The solution of the inequality is \(k\leq7\). On the number - line, there is a closed circle at \(7\) and a ray extending to the left.
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5. question: two adjacent angles sum to 90 degrees. if the angle measur…
\(x = 9\), so the answer is A.
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find the measure of the complement and the supplement of ( 8^{circ} ). …
\(82\)
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if ( x = 34^{circ} ), find the measure of the angle in which ( ?^{circ}…
\(56^{\circ}\)
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7. question: two angles form a straight line. one angle measures 2x + 1…
A. \(x = 35\)
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which statement proves that pqrs is a parallelogram? the slopes of \\( …
The slopes of \(\overline{RS}\) and \(\overline{QP}\) are both \(3\) and \(SP = RQ=\sqrt{45}\).
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what is the measure of the missing angle?
\(50^{\circ}\)
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1 fill in the blank 20 points the unit circle is a circle with radius o…
1; origin
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what is the sum of the angles inside a triangle?
\(180\)
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what is the name of this kind of triangle? right isosceles equilateral …
B. Isosceles
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got it? 2. can you prove that the quadrilateral is a parallelogram base…
a. No. The given information (\(\overline{EF}\cong\overline{GD},\overline{DE}\parallel\overline{FG}\)) does not satisfy the criteria (a pair of opposite sides that are both parall…
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how many acute angles must an acute triangle have?
3
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a scalene triangle has______ all sides congruent 3 different angle name…
no congruent sides
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a triangle with 3 congruent sides is called a(n)________ isosceles tria…
Equilateral Triangle
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state the triangle congruence theorem that proves the triangles congrue…
ASA
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classify the triangle by angles and sides. acute isosceles right isosce…
Right Scalene
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classify the triangle by angles and sides. obtuse isosceles right scale…
Obtuse Scalene
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what are possible coordinates of point f if \\( \\triangle def \\) is c…
# Explanation: ## Step1: Analyze the length of sides in \(\triangle ABC\) Assume \(A(- 4,0)\), \(B(-5,-5)\), \(C(0,-5)\). The length of \(AB=\sqrt{(-4 + 5)^{2}+(0 + 5)^{2}}=\sqrt{…
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classify the triangle by angles and sides
Obtuse Isosceles
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read the excerpt from its our world, too!: young people who are making …
The crowd is moved by the students’ compassion.
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classify the triangle by angles and sides.
Right Isosceles
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in the diagram, ( ae = 2ac ) and ( angle bac cong angle dae ). what add…
AD = 2AB
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m∠abc + m∠bac + m∠acb when △abc is an isosceles triangle with ab = ac m…
\(180^{\circ}\to m\angle ABC + m\angle BAC + m\angle ACB\) \(55^{\circ}\to m\angle ABC\) when \(m\angle BAC = 70^{\circ}\) and \(\triangle ABC\) is isosceles with \(AB = AC\) \(45…
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communicate your answer 3. when two parallel lines are cut by a transve…
Corresponding angles, alternate interior angles, alternate exterior angles, and vertical angles.
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the vertices of (\triangle abc) are (a(1,-2)), (b(1,1)), and (c(5,-2)).…
B. \(9, 12,\) and \(15\) units
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given: rstu is a rectangle with vertices r(0,0), s(0,a), t(a,a), and u(…
B. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it's a square
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15 image.png 15/8 15/17 17/15 8/17 8/15 17/8 tanθ = sinθ = cosθ =
\(\tan\theta=\frac{8}{15}\), \(\sin\theta=\frac{8}{17}\), \(\cos\theta=\frac{15}{17}\)
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find the measures of the following angles in the kite shown below. note…
\(a = 61\), \(b = 137\)
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question 1 - 14 in the diagram above ( \triangle fghcong\triangle str )…
\(x = 61\), \(y=9\)
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1 matching 20 points given the following, match the trig function to it…
\(\tan\theta=\frac{8}{15}\), \(\sin\theta=\frac{8}{17}\), \(\cos\theta=\frac{15}{17}\)
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the correct answer in the box. an airplane takes off from point a in a …
\(6500\)
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in the diagram, ( fh=\frac{1}{3}ac ) and ( 3fg = ab ). what additional …
\(\frac{BC}{GH}=3\)
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2. question: two angles form a right angle. one angle measures 7x - 3 a…
2. B. \(x = 7\) 3. A. \(x = 18\) 4. B. \(x = 17.5\)
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points a, b, and c form a triangle. complete the statements to prove th…
The reason for \(\angle3\cong\angle5\) and \(\angle1\cong\angle4\) is the Alternate Interior Angles Theorem. The reason for \(m\angle1 = m\angle4\) and \(m\angle3 = m\angle5\) is …
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is △abc congruent to △def? no △abc is not congruent to △def. you can no…
Yes \(\triangle ABC\) is congruent to \(\triangle DEF\). \(\triangle ABC\) was reflected over the line \(y=-3\), then translated 3 units to the left and 1 unit down to get to \(\t…
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proof: 1. quadrilateral defg is a parallelogram. - given 2. \\( \\overl…
D. Alternate Interior Angles Theorem
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question 1 - 12 use the diagram to answer the questions and complete th…
For Step 3: SSS Postulate. For Step 4: Corresponding parts of congruent triangles are congruent.
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determine the missing reasons in the proof. statement reason abdc is a …
For $\triangle CDA\cong\triangle BDA$: SSS criterion. For $\triangle CED\cong\triangle BED$: SAS criterion.
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the correct answers. △lmn has vertices l(-2,4), m(3,2), and n(1,-3). wh…
right, isosceles
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16 what is the missing step in this proof? a. ∠abc ≅ ∠dbe b. ∠bca ≅ ∠bd…
A. \(\angle ABC\cong\angle DBE\)