Geometry A final exam
Which transformations will carry figure ABCD onto itself? Select all that apply.
A 360° rotation about the midpoint of AB. A 180° rotation about the intersection of the two diagonals of ABCD.
Triangle ABC is a right triangle. Select and drag the ratios to the empty boxes to correctly complete each equation.
Sin B - 8/17 Cos A - 8/17 Cos B- 15/17 Tan B - 8/15
How can you prove that DB/AD = EC/AE?
1. ADE ~ ABC 2. AB/AD = AC/AE 3. 1 + DB/AD = 1 + EC/AE
How can it be proven that the diagonals bisect each other? Drag the tiles to the empty boxes to complete each part of the proof correctly.
1. Given 2. alternate interior 3. vertical 4. XXX ASA
In the xy-plane, a line segment is dilated by a scale factor of 22. The dilation is centered at a point not on the line segment.
1. Parallel 2. twice
Consider △FGH and △FJK. Select from the drop-down lists to correctly complete the sentences.
1. XXX 2 pairs XXX 3 pairs 1. (0 pairs have to be correct) 2. dilation 3. 2 pairs
How could you prove ∠CAB≅∠CDB? Drag tiles to the empty boxes to complete the proof.
1. alternate interior angles 2. corresponding angles 3. transitive property
How can it be proven that a pair of corresponding angles are congruent? Drag a phrase to each empty box to complete each sentence correctly.
1. it is given 2. they are vertical angles 3. they are alternate exterior angles 4. of the transitive property
What reasons complete the proof of ∠B≅∠C? Drag the phrases to the empty boxes to complete the proof correctly.
1. of the definition of an angle bisector 2. of the reflective property 3. of SAS 4. corresponding parts of congruent triangles are congruent
In the diagram, JM ≅ PR, MK ≅ RQ, and KJ ≅ QP. Drag a tile to each empty box to complete the sentences correctly.
1. reflection 2. are
Naomi used the figure shown to help prove the Pythagorean Theorem. In the figure, both △ACD△ and △CBD△are similar to △ABC△. term-28 She began by correctly setting up the proportions ac=xa and bc=yb and cross-multiplying to get the equations a^2=xc and b^2=yc. What should Naomi do next?
1. sum 2. c
Gaja wants to determine if there is a series of rigid transformation that can be used to show △ABC≅△FED. Select an option from each dropdown menu to correctly complete Gaja's line of reasoning.
1. translate 2. down 3 units
Randy wants to determine whether these two rectangles are congruent using only rigid transformations. Select from the drop-down lists to complete each sentence correctly.
1. translation 2. rotation
Prove that the interior angles of a triangle sum to 180 degrees. Drag a tile into each box to complete the proof correctly.
1. when parallel lines are cut by transversal, alternate interior angles are congruent 2. of the substitution property of equality
AB has endpoints at (2,3) and (2,5). After a dialation with a center at the origin and a scale factor of 1/5, what would be the length of the image of AB?
2/5 units
A ramp has a height of 5.8 feet and an angle of 80°. A sketch of the ramp is shown. What is the length of the ramp, y, to the nearest tenth of a foot?
33.4
Use the fact that sin38°≈0.6157to answer this question.
52
To prove △ADB ≅ △CDB, she wants to verify that corresponding pairs of sides and corresponding pairs of angles are congruent using just one rigid transformation. Which of the following transformations would accomplish this task?
A reflection of △CDB about diagonal BD.
After performing some set of rigid transformations, which of the following conditions must be true to verify that the two triangles are congruent?
All pairs of corresponding sides are congruent.
Which ratios are equivalent to tanF? Select all that apply.
EL/EF OS/OJ
Rectangle ABCD is in the coordinate plane. Which of the following is a valid definition of a reflection of rectangle ABCD?
Every point X on ABCD is mapped to a new point X′ such that the distance from X to the line of reflection is the same as the distance from X′ to the line of reflection.
In the figure, QN is the perpendicular bisector of LM. Which of the following can be used to prove that point P is equidistant from the endpoints of LM?
First, prove that △LNP ≅ △MNP by the side-angle-side theorem. Second, prove that point P is equidistant from the endpoints of LM by showing that PL ≅PM because corresponding parts of congruent triangles are congruent.
What is the length of CD? If the perimeter of triangle ABC is 27.6 cm, what is the perimeter, in centimeters, of triangle BCD?
Part A - 3.75 cm Part B - 17.25
A 22-foot ladder leans against a building. The distance between the bottom of the ladder and the base of the building is 9 feet. Which statement is true when finding the height, in feet, where the ladder touches the building, h?
The equation to find h is 9^2 + h^2 = 22^2 and h is about 20.1 feet.
Which statement is the most precise and correct definition of parallel lines?
Two lines are parallel if they are at a constant distance apart.
Figure ABCD is a trapezoid. Which sequence of transformations will carry figure ABCD onto itself?
a reflection across the line joining the midpoints of DA and CB followed by a second reflection about the line joining the midpoints of DA and CB
Which sequence of transformations will carry △QRS onto △Q′R′S′?
a translation left 3 units and down 6 units
Triangle ABC and Triangle DEF are similar triangles. Which of the following statements are true? Select all that apply.
m∠B = m∠E If DF = 16, then DE = 12. AB/BC = DE/EF
What is the term for two lines in a plane that intersect at a 90° angle?
perpendicular lines
Which transformations preserve distances between points and angle measures? Select all that apply.
reflection across the line y=x clockwise rotation of 90° about the origin translation 4 units down
Which statement will help to show that ∠2≅∠4?
∠1 is supplementary to ∠2, and ∠1 is supplementary to ∠4.
Consider △ABC and △DEF, both of which lie in the xy-coordinate plane. The pre-image, △ABC, is rotated 180° about the point (0,2)to obtain the image, △DEF. Which of the following statements are true? Select all that apply.
∠B ≅ ∠E AC ≅ DF BC ≅ EF
