Geometry Unit Test (88%)

Given: ∠BCD is right; BC ≅ DC; DF ≅ BF; FA ≅ FE Which relationships in the diagram are true? Check all that apply.

2, 3, 5

Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ? What is the perimeter of triangle YXZ?

6.4

Which pair of triangles can be proven congruent by SAS?

A.

Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM. If MV measures 3 cm, which other segment must measure 3 cm?

A. AF

How can a translation and a reflection be used to map ΔHJK to ΔLMN?

B. Translate K to N and reflect across the line containing JK.

Two rigid transformations are used to map ΔHJK to ΔLMN. The first is a translation of vertex H to vertex L. What is the second transformation?

B. a rotation about point H

Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS. Which relationship in the diagram is true?

B. △RMS ≅ △RQS by AAS

Triangle GHJ is rotated 90° about point X, resulting in triangle STR. Which congruency statement is true?

C. TS ≅ HG

Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?

D. HL

Is there a series of rigid transformations that could map ΔQRS to ΔABC? If so, which transformations could be used?

D. Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is required to map DEF onto GHJ?

D. translation

Are the triangles congruent? Why or why not?

A. Yes, all the angles of each of the triangles are acute.

Is MNL ≅ QNL? Why or why not?

A. Yes, they are congruent by either ASA or AAS.

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

A. ΔXYZ ≅ ΔTUV

Quadrilateral ABCD is translated down and left to form quadrilateral OLMN. If AB = 6 units, BC = 5 units, CD = 8 units, and AD = 10 units, what is LO?

B. 6 units

The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map MNP onto TSR?

C

Two rigid transformations are used to map ABC to QRS. The first is a translation of vertex B to vertex R. What is the second transformation?

C

What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem?

C. LOA ≅ LMA

Could ΔJKL be congruent to ΔXYZ? Explain.

C. No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

Which congruence theorem can be used to prove △WXS ≅ △YZS?

C. SAS

Quadrilateral LMNO is reflected over the line as shown, resulting in quadrilateral CDAB. Given the congruency statement LMNO ≅ CDAB, which segment corresponds to ML?

D. DC

In the diagram, ∠J ≅ ∠M and JL ≅ MR. What additional information is needed to show ΔJKL ≅ △MNR by SAS?

D. JK ≅ MN