Question 1(Multiple Choice Worth 1 points)

Question

(03.03 MC)

Triangles BAC and EDC intersect at point C; line f intersects triangles BAC and EDC at point C; angles BAC and EDC are right angles.

If m∠ABC = 53° and m∠ECD = 37°, which statement explains whether the AA similarity postulate can be used to determine whether ΔBAC ~ ΔEDC?

Yes, the AA similarity postulate can be used because a reflection over line f will establish that ∠ABC ≅ ∠DEC.
Yes, the AA similarity postulate can be used because a reflection over line f will establish that segment AB ≅ segment DE.
No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.
No, the AA similarity postulate cannot be used because a reflection over line f will establish that segment AB and segment DE are not congruent.
Question 2(Multiple Choice Worth 1 points)
(03.03 LC)

If a figure has been dilated by a scale factor of 2, which transformation could be used to prove the figures are similar using the AA similarity postulate?

A reflection to map at least two sides of the image to two sides of the pre-image.
A series of dilations to map at least two angles of the image to two angles of the pre-image.
A rotation to map at least two sides of the image to two sides of the pre-image.
A series of translations to map at least two angles of the image to two angles of the pre-image.
Question 3(Multiple Choice Worth 1 points)
(03.03 MC)

If ΔMNL is rotated 180° about point N, which additional transformation could determine if ΔONP and ΔMNL are similar by the AA similarity postulate?

Segments OM and LP intersect at point N; triangles are formed by points LNM and ONP; line k intersects with both triangles at point N.

Reflect ONP over line k.
Reflect M′N′L′ over line k.
Dilate ONP from point N by a scale factor of segment NP over segment NL.
Dilate M′N′L′ from point N by a scale factor of segment NP over segment NL
Question 4(Multiple Choice Worth 1 points)
(03.03 MC)

Shaun drew ΔLMN, in which m∠LMN = 90°. He then drew ΔPQR, which was a dilation of ΔLMN by a scale factor of 3 from the center of dilation at point M. Which of these can be used to prove ΔLMN ~ ΔPQR by the AA similarity postulate?

segment LM = 3segment PQ; this can be confirmed translating point P to point L.
segment MN = 3segment QR; this can be confirmed translating point R to point N.
m∠P ≅ m∠N; this can be confirmed by translating point P to point N.
m∠R ≅ m∠N; this can be confirmed by translating point R to point N.
Question 5(Multiple Choice Worth 1 points)
(03.03 MC)

If a translation maps ∠I onto ∠K, which of the following statements is true?

Triangles HGI and JGK; point H is between points J and G on segment JG, and point I is between points G and K on segment GK.

segment HI is twice the measure of segment JK.
segment GH is twice the measure of segment GJ.
Triangles ΔGHI and ΔGJK are not similar.
∠H ≅ ∠J
Question 6(Multiple Choice Worth 1 points)
(03.03 MC)

Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

triangles EFG and YXZ in which triangle YXZ is larger than EFG

segment EF ~ segment XZ.
The measure of segment YZ is three times the size of segment EG.
segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX
There is a sequence of rigid motions that map ΔEFG onto ΔYXZ.
Question 7(Multiple Choice Worth 1 points)
(03.03 MC)

Which of the following completes the proof?

Triangles ABC and EDC are formed from segments BD and AC, in which point C is between points B and D and point E is between points A and C.

Given: Segment AC is perpendicular to segment BD

Prove: ΔACB ~ ΔECD

Reflect ΔECD over segment AC. This establishes that ∠ACB ≅ ∠E′C′D′. Then, ________. This establishes that ________. Therefore, ΔACB ~ ΔECD by the AA similarity postulate.

translate point E′ to point A; ∠E′D′C′ ≅ ∠ABC
translate point D′ to point A; ∠E′D′C′ ≅ ∠BAC
translate point D′ to point A; ∠D′E′C′ ≅ ∠BAC
translate point E′ to point A; ∠D′E′C′ ≅ ∠BAC
Question 8(Multiple Choice Worth 1 points)
(03.03 HC)

Which of the following explains how ΔAEB could be proven similar to ΔDEC using the AA similarity postulate?

Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E.

∠AEB ≅ ∠CED because vertical angles are congruent; reflect ΔCED across segment FG, then translate point D to point A to confirm ∠EAB ≅ ∠EDC.
∠AEB ≅ ∠CED because vertical angles are congruent; rotate ΔCED 180° around point E, then dilate ΔCED to confirm segment EB ≅ segment EC.
∠AEB ≅ ∠DEC because vertical angles are congruent; rotate ΔCED 180° around point E, then translate point D to point A to confirm ∠EAB ≅ ∠EDC.
∠AEB ≅ ∠DEC because vertical angles are congruent; reflect ΔCED across segment FG, then dilate ΔCED to confirm segment EB ≅ segment ED
Question 9(Multiple Choice Worth 1 points)
(03.03 MC)

In ΔEFG and ΔYXZ, m∠F ≅ m∠X and m∠E ≅ m∠Y. If m∠E = 62° and m∠X = 80°, what is the measure of ∠F?

triangles EFG and YXZ in which triangle YXZ is larger than EFG

38°
62°
80°
142°
Question 10(Multiple Choice Worth 1 points)
(03.03 LC)

Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?

Segments OM and LP intersect at point N; triangles are formed by points LNM and ONP; line k intersects with both triangles at point N.

Use a rigid transformation to prove that ∠OPN ≅ ∠MLN.
Use rigid and nonrigid transformations to prove segment PN over segment MN = segment LN over segment ON.
Use a rigid transformation to prove that ∠NPO ≅ ∠LNM.
Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.

Answer 1

Sure! Here are the answers to your questions:

Question 1:
Answer: No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.

Question 2:
Answer: A series of translations to map at least two angles of the image to two angles of the pre-image.

Question 3:
Answer: Reflect ONP over line k.

Question 4:
Answer: m∠R ≅ m∠N; this can be confirmed by translating point R to point N.

Question 5:
Answer: ∠H ≅ ∠J

Question 6:
Answer: segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Question 7:
Answer: translate point D′ to point A; ∠E′D′C′ ≅ ∠BAC

Question 8:
Answer: ∠AEB ≅ ∠CED because vertical angles are congruent; reflect ΔCED across segment FG, then translate point D to point A to confirm ∠EAB ≅ ∠EDC.

Question 9:
Answer: 80°

Question 10:
Answer: Use a rigid transformation to prove that ∠NPO ≅ ∠LNM.

Please let me know if you need any additional explanations or if you have more questions!