Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
-
lesson 1 | session 2 the photo shows a small coin. the scale from the a…
Caleb's actual height is \(48\) inches.
-
practice using scale to find distances study the example showing how to…
The drawing is \(2.8\) inches wide and \(3.5\) inches long.
-
a drawing of a basement uses the same scale as the example. the basemen…
The drawing is $2.8$ inches wide and $3.5$ inches long.
-
solve the inequality and graph the solution. 7 > 2a + 3 to draw a ray, …
The solution of the inequality is \(a < 2\). On the number - line, there is an open circle at \(2\) and a ray extending to the left.
-
the diagram shows a triangle. what is the value of c? c = °
\(4\)
-
solve the inequality and graph the solution. 3y + 20 > 14 to draw a ray…
The solution of the inequality \(3y + 20>14\) is \(y>-2\). On the number - line, there is an open circle at \(-2\) and a ray extending to the right.
-
the diagram shows a triangle. what is the value of t?
\(t = 17\)
-
solve the inequality and graph the solution. 10 + 6y > 4 to draw a ray,…
The solution of the inequality \(10 + 6y>4\) is \(y>-1\). On the number - line, we have an open circle at \(-1\) and a ray extending to the right.
-
solve the inequality and graph the solution. 20 < 2 + 3d to draw a ray,…
The solution of the inequality is \(d > 6\). On the number - line, we plot an open circle at \(d = 6\) (because \(6\) is not included in the solution set) and draw a ray to the ri…
-
the diagram shows a triangle. what is the value of y? y =
\(y = 22\)
-
solve the inequality and graph the solution. 1 > -p - 1 to draw a ray, …
The solution of the inequality \(1>-p - 1\) is \(p > - 2\). On the number - line, we plot an open circle at \(p=-2\) (because the inequality is strict, i.e., \(p eq - 2\)) and dr…
-
the diagram shows a triangle. what is the value of z? z = submit
\(z = 8\)
-
solve the inequality. c + 15 ≤ -7 the solution is: graph the solution.
$c\leq-22$ To graph the solution: - Place a closed circle at $-22$ (because the inequality is $\leq$, so $-22$ is included in the solution set). - Shade to the left of $-22$ (sinc…
-
solve the inequality and graph the solution. 1 + 9z < 19 to draw a ray,…
The solution of the inequality \(1 + 9z<19\) is \(z < 2\). On the number - line, there is an open - circle at \(2\) and a ray extending to the left of \(2\).
-
the diagram shows a triangle. what is the value of p? p =
\(2\)
-
solve the inequality and graph the solution. \\( \\frac { c } { 2 } - 1…
The solution of the inequality is \(c\leq4\). On the number - line, there is a closed circle at \(4\) and an arrow pointing to the left.
-
the diagram shows a triangle. what is the value of s? s = ° submit
\(20\)
-
what is the slope of this line? simplify your answer and write it as a …
\(0\)
-
the diagram shows a triangle. what is the value of a? a =
\(6\)
-
solve the inequality and graph the solution. 7 < -17 + 3r to draw a ray…
The solution of the inequality is \(r>8\). On the number - line, there is an open circle at \(8\) and a ray extending to the right.
-
3. the triangles are congruent. which sequence of rigid motions will ta…
A. Translate \(XYZ\) using directed line segment \(YC\). Rotate \(X'Y'Z'\) using \(C\) as the center so that \(X'\) coincides with \(B\). Reflect \(X''Y''Z''\) across line \(CB\).…
-
the diagram shows a triangle. what is the value of w? w =
\(4\)
-
solve the inequality and graph the solution. 9 + 2t < 1 to draw a ray, …
The solution of the inequality is \(t < - 4\). On the number - line, we plot an open circle at \(-4\) (because the inequality is strict, \(t eq - 4\)) and draw a ray to the left …
-
the diagram shows a triangle. what is the value of s? s = square^{circ}
\(s = 2\)
-
the diagram shows a triangle. what is the value of b? b =
\(11\)
-
solve the inequality and graph the solution. -9 + 6r > 9 to draw a ray,…
The solution of the inequality is \(r>3\). On the number - line, there is an open - circle at \(3\) and a ray extending to the right.
-
question solve the inequality and graph the solution on the line provid…
Inequality Notation: \(x\geq - 1\) To graph on the number line: - Draw a number line. - Place a closed circle (because the inequality is \(\geq\)) at \(-1\). - Shade to the right …
-
lesson 3 practice problems 1. triangle abc is congruent to triangle edf…
B. Angle \(B\) coincides with angle \(D\), C. Segment \(AC\) coincides with segment \(EF\), E. Segment \(AB\) coincides with segment \(ED\) 2. a.
-
what is the length of the hypotenuse? if necessary, round to the neares…
\(2.2\)
-
which equation can be used to find the value of x? x + 45 + 40 = 180 x …
\(x = 45 + 40\)
-
solve the inequality and graph the solution. 2 + 4d ≥ 10 to draw a ray,…
The solution of the inequality \(2 + 4d\geq10\) is \(d\geq2\). On the number - line, plot a closed circle at \(2\) and draw a ray to the right.
-
what is the length of the missing leg? if necessary, round to the neare…
\(4.9\)
-
select the simple predicate. he circled his favorite line of the poem.
circled
-
what is the length of the hypotenuse? if necessary, round to the neares…
\(7.5\)
-
state the quadrant or axis that each point lies in. 5) ( l(-2,1) ) ( k(…
5) \(L(-2,1)\) is in Quadrant II, \(K(-3,-2)\) is in Quadrant III, \(J(3,1)\) is in Quadrant I. 6) \(T(-3,5)\) is in Quadrant II, \(U(1,0)\) is on the \(x -\)axis, \(V(-5,5)\) is …
-
olve the inequality and graph the solution on the line provided. 7 + 4x…
Inequality Notation: \(x\leq - 1\) For the number - line: Plot a closed circle at \(x = - 1\) (because the inequality is \(\leq\)) and draw a line to the left of \(x=-1\) towards …
-
find the height of a pyramid with a volume of 128 cm³ if the base is a …
\(6\)
-
what is the length of the missing leg? if necessary, round to the neare…
\(21\)
-
use the image to answer the question. prove that the diagonals of recta…
The diagonals \(LN\) and \(OM\) of rectangle \(LMNO\) are congruent.
-
find the volume of the rectangular prism. v = ? in³
\(352\)
-
what is the length of the missing leg? if necessary, round to the neare…
\(21\)
-
19. a square has an area of $81in^{2}$. what is the perimeter of the sq…
36 in
-
17. the formula for the perimeter of a rectangle with length l and widt…
\(L = 10,W = 9\)
-
graph the image of square tuvw after a rotation 180° clockwise around t…
Plot the points \((-5,2)\), \((-6,2)\), \((-6,1)\), \((-5,1)\) and connect them.
-
in the right triangle △rst, the legs rs and st have lengths 6 cm and 8 …
C. 10
-
in the diagram of circle o, what is the measure of ∠abc? 27° 54° 108° 1…
\(54^{\circ}\) (the second option)
-
graph the image of \\( \\triangle k l m \\) after a rotation \\( 270^{\…
Plot the points \(K'(-9,1)\), \(L'(-6,1)\), \(M'(-6,0)\) and connect them.
-
in circle z, what is m∠2? 70° 133° 140° 147°
\(140^{\circ}\) (the third option)
-
in \\( \\triangle abc \\), the measure of \\( \\angle a \\) is \\( 40 ^…
\(\angle C = 75^{\circ}\), so the answer is D. \(75^{\circ}\)
-
7. brian wants to re - tile his bathroom floor. he does not need to til…
38 sq ft
-
in circle y, what is ( mangle1 )?
\(31^{\circ}\)
-
in the diagram of circle p, ( mangle xyz ) is ( 72^{circ} ). what is th…
\(108^{\circ}\)
-
which equation is correct regarding the measure of ∠1? ○ ( m angle 1 = …
\(m\angle1=\frac{1}{2}(b - d)\) (the third option)
-
which equation is correct regarding the measure of ∠mnp? ○ ( m angle mn…
\(m\angle MNP=\frac{1}{2}(z - y)\) (the fourth option)
-
graph the image of \\( \\triangle cde \\) after a reflection over the \…
The coordinates of the reflected triangle \(\triangle C'D'E'\) are \(C'(-7,-6)\), \(D'(2,-6)\) and \(E'(-7,-3)\). Plot these points and connect them.
-
3. larry has a square porch with sides of length 9 feet. he plans to en…
51
-
a secant and a tangent meet at a 90° angle outside the circle. what mus…
$180^{\circ}$
-
graph the image of ( q(-5,-8) ) after a reflection over the ( x )-axis.
The image of \(Q(-5,-8)\) after reflection over the \(x -\)axis is \(Q'(-5,8)\).
-
19.) part a: write an algebraic expression that represents the perimete…
Part A: \(2[(16x - 5)+(4x + 2)]\) Part B: \(40x - 6\)
-
a raft is crossing a river. the raft is being paddled at a speed of 3 f…
C. 500
-
6. describe a sequence of transformations that would map triangle a to …
Reflect Triangle \(A\) over the \(y\) - axis and then translate the resulting triangle \(6\) units to the right.
-
what is ( mwidehat{po} )? ( 128^{circ} ) ( 173^{circ} ) ( 192^{circ} ) …
\(173^{\circ}\)
-
circle x is shown in the diagram. which equation can be used to solve f…
\(m\angle1=\frac{1}{2}(a + b)\) (the second option)
-
find xy. 1. 2. 3. 4. find the value x. 5. 6. 7. 8. point c is between a…
1. \(XY = 16\) 2. \(ZY = 7\) 3. \(XY = 16\) 4. \(XY = 9\) 5. \(x = 10\) 6. \(x = 8\) 7. \(x = 3\) 8. \(x = 1\) 9. \(x = 2\), \(AC = 22\), \(CB = 10\), \(AB = 32\) 10. \(x = 1\), \…
-
in the diagram, ( a parallel b ) and ( e parallel f ), forming a parall…
We have proved that the opposite sides of the parallelogram (formed by \(a\parallel b\) and \(e\parallel f\)) are congruent. For example, using the ASA congruence criterion on \(\…
-
7. triangle abc is defined by the coordinates ( a(5,1) ), ( b(3,-1) ), …
For part (a), plot \(A(5,1)\), \(B(3,-1)\), \(C(2,4)\) and connect them. For part (b), plot \(A''(-3,1)\), \(B''(-1,-1)\), \(C''(0,4)\) and connect them.
-
1. if \\( \\angle k \\) and \\( \\angle b \\) are supplementary and \\(…
1. \(107^{\circ}\) 2. \(85^{\circ}\) 3. \(92^{\circ}\) 4. \(6\) 5. \(\frac{30}{7}\) 6. \(-6\)
-
the perimeter of a rectangle is 38 inches. if the length is 3 inches mo…
8 inches
-
practice problems 1 angle abc is taken by a dilation with center p and …
1. The measure of \( \angle A'B'C'\) is \(21^{\circ}\). 2. B. \(m\), C. \(n\), E. \(p\)
-
a satellite views the earth at an angle of 20°. what is the arc measure…
\(160^{\circ}\)
-
3 from unit 3, lesson 4 angle abc is taken by a dilation with center p …
\(21^{\circ}\)
-
what is the measure of arc qsr? 70°
\(250\)
-
mark is playing pool. on a pool table there are 6 holes that you have t…
a. By the perpendicular bisector theorem, since \(GH\) is the perpendicular bisector of \(FC\) and \(I\) is on \(GH\), \(IF = IC\). b. Point \(J\) is equidistant from \(F\) and \(…
-
lesson 4 - 2: exit ticket in the figure shown, what is the value of x? …
\(x=-27\)
-
lesson 4 - 2: exit ticket which of the following statements is incorrec…
The measure of each angle of an equilateral triangle is \(120^{\circ}\)
-
practice problems 7 problems 1 here are triangles abc and abc. what is …
B. \(40^{\circ}\) For the second problem (assuming we are still in the Geometry sub - field of Mathematics):
-
use the image to answer the question. lines \\( \\overline { a c } \\) …
\(x = 6\)
-
lesson 4 - 2: do now (day 2) what is the value of x? 45° 60° 80° 90°
\(45^{\circ}\)
-
8. macari looked at the two triangles below and stated that the triangl…
No, I do not agree with Macari. A reflection over the \(x\) - axis changes the \(y\) - coordinate of a point \((x,y)\) to \((x, - y)\). The vertex - to - vertex correspondence (e.…
-
use the image to answer the question. given the rectangle ( a b c d ) a…
\(1\)
-
lesson 4 - 2: do now (day 2) based on the isosceles triangle theorem, w…
\(51.5^{\circ}\)
-
what is the measure of angle aoc? 42° 58° 66° 79°
# Explanation: ## Step1: Find the measure of arc \(DC\) The measure of an arc is equal to the measure of its central angle. The sum of arcs \(DE\) and \(EC\) (where \(EC\) is rela…
-
topic 4 - 2: do now what is ( mangle b )? 121 67 59 53
\(59\)
-
topic 4 - 2: do now what is the sum of the angles in a triangle? i
\(180\)
-
9. graph the image of abc after a reflection over the x - axis and a tr…
Plot the points \(A''(-1,-3)\), \(B''(2,-1)\), \(C''(-1,-1)\) on the coordinate - plane and connect them.
-
if quadrilateral wxyz is a parallelogram, which segment of the figure m…
\(\overline{XV}\)
-
what are the three types of rigid motions? and turning reflection rotat…
reflection, rotation, translation
-
find the vertex and focus of the parabola: x² - 10x - 12y - 23 = 0 vert…
Vertex \(=(5,-4)\) Focus \(=(5,-1)\)
-
topic 3 review- do now possible points: 3 match each transformation wit…
\(R_{(x - axis)}(x,y)=(x,-y)\) \(R_{(y - axis)}(x,y)=(-x,y)\) \(r_{90^{\circ}}(x,y)=(-y,x)\) \(r_{180^{\circ}}(x,y)=(-x,-y)\) \(r_{270^{\circ}}(x,y)=(y,-x)\) \(T_{\langle2,3 angle…
-
graph the triangle rotated 90° counterclockwise about the origin
Let the original vertices of the triangle be \(A(2,2)\), \(B(7,1)\), \(C(7, - 4)\). After a \(90^{\circ}\) counter - clockwise rotation about the origin, the new vertices are \(A'…
-
given: (overline{lm}congoverline{on}) and (overline{lo}congoverline{mn}…
The proof is assembled as above to show that \(LMNO\) is a parallelogram.
-
directions: determine whether each pair of triangles is similar. if the…
yes they are similar by AA similarity
-
erik draws quadrilateral (abcd). if side (ab = 40x), side (bc = 4 + 3y)…
\(x = 1\) and \(y = 4\) (the third option)
-
directions: determine whether each pair of triangles is similar. if sim…
The triangles are not proportional, so there is not enough information to conclude similarity.
-
type the correct answer in the box. use numerals instead of words. if n…
\(\frac{1}{2}\)
-
directions: determine whether each pair of triangles is similar. if the…
yes they are similar by SSS similarity
-
solve for x. figure is not drawn to scale, 7x 140 x = 20 add work > nex…
\(x = 10\)
-
select from the drop - down menus to correctly complete the sentence th…
First blank: right; Second blank: down
-
2. triangle abc and pqr are shown below in the coordinate plane. descri…
First, reflect triangle \(ABC\) over the \(x -\)axis. Then, translate the reflected triangle \(5\) units to the right and \(1\) unit down.
-
use the image to answer the question. olivia wrote a paragraph proof to…
1. I am given that quadrilateral \(MNOP\) is a parallelogram. I know that opposite sides of a parallelogram are congruent because of the definition of a parallelogram, so \(\overl…