Triangle Congruence: SAS Answers

Which rigid transformations would map ΔJKL onto ΔPQR? Select the three correct answers.

To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?

What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

Can ΔTSR and ΔQRS be proven congruent by SAS?

Given: C is the midpoint of BD.

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?

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?

translatereflect✔ rotate

angles BCA and DCA form a linear pair✔ angle BCA is congruent to angle DCAsegment AC is perpendicular to segment BD

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.

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.

First, translate vertex A to vertex [___].

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.

✔ DFB and DECECD and DBCFDC and EDB