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Triangle Congruence: SAS Assignment and Quiz

Terms in this set (19)

Which rigid transformation(s) would map ΔJKL onto ΔPQR?
a reflection only
a rotation and a reflection
a translation and a reflection
To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?
∠DFE ≅ ∠ DFG
The frame of a bridge is constructed of triangles, as shown below.


What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.
UV = 14 ft and m∠TUV = 45°
ST = 20 ft, UV = 14 ft, and m∠UST = 98°
How can ΔABC be mapped to ΔXYZ?

First, translate vertex A to vertex __.

Next, ________ ΔABC to align the sides and angles.
X
rotate
Can ΔTSR and ΔQRS be proven congruent by SAS?
no, because not enough is information given to prove the triangles congruent by SAS
Given: C is the midpoint of BD.

Prove: ΔACB ≅ ΔACD


Complete the two-column proof.
definition of midpoint

angle BCA is congruent to angle DCA
Given: RT || SP, RQ ≅ QP, RP bisects ST at Q
Prove: ΔRQT ≅ ΔPQS


Tamir is working to prove the triangles congruent using SAS. After stating the given information, he states that TQ ≅ QS by the definition of segment bisector. Now he wants to state that ∠RQT ≅ ∠PQS. Which reason should he use?
vertical angles theorem
Given: ΔDFE is isosceles with base FE; FB ≅ EC.

Prove: ΔDFB ≅ ΔDEC


Complete the missing parts of the paragraph proof.



We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because ___________. Segment DF is congruent to segment __ by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles _______________, are congruent by the isosceles triangle theorem. Therefore, triangles ____________ are congruent by SAS.
it is given
DE
DFE and DEF
DFB and DEC
Consider ΔWXY and ΔBCD with ∠X ≅∠C, WX ≅ BC, and WY ≅ BD.

Can it be concluded that ΔWXY ≅ ΔBCD by SAS? Why or why not?
no, because the corresponding congruent angles listed are not the included angles
Which of these triangle pairs can be mapped to each other using both a translation and a rotation about C?
D
The proof that ΔACB ≅ ΔECD is shown.

Given: AE and DB bisect each other at C.
Prove: ΔACB ≅ ΔECD





What is the missing statement in the proof?
∠ACB ≅ ∠ECD
Triangles RQS and NTV have the following characteristics:

• Right angles at ∠Q and ∠T
• RQ ≅ NT

Can it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not?
No, it is necessary to know that another set of corresponding sides is congruent.
Which of these triangle pairs can be mapped to each other using a single translation?
D
How can ΔWXY be mapped to ΔMNQ?



First, translate vertex W to vertex M.

Next, reflect ΔWXY across the line containing
line segment WX
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?
a rotation about point H
Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?
A
The proof that ΔEFG ≅ ΔJHG is shown.

Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.

Prove: ΔEFG ≅ ΔJHG


What is the missing statement in the proof?
∠GFE ≅ ∠GHJ
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
∠L ≅ ∠R
If CB bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Check all that apply.
m∠ABC = 125° and AB ≅ DB
ΔACD is isosceles with base AD
CD = 52 cm
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