1. DABC and DDCB 2. DEFG and DHGF 3. DJML and DNKL

Name

Class

Date

Congruence in Overlapping Triangles

4-7

Practice

Form G

For Exercises 1–6, separate and redraw the indicated triangles. Identify any common angles or sides.

4. DBYA andDCXA 5. DGEH and DFEH 6. DMPN and DMOQ

1. DABC and DDCB 2. DEFG and DHGF 3. DJML and DNKL

In each diagram in Exercises 7–12 the given triangles are congruent. Identify their common side or angle.

10. DQTR and DSRT 11. DEGH and DEGF 12. DYNI and DYPZ

7. DADC and DBCD 8. DKNJ and DKML 9. DUXV and DVWU

13. Open-Ended Draw a diagram of a pair of triangles that share a common angle and a common side.

Prentice Hall Gold Geometry • Teaching Resources

Name

Class

Date

Congruence in Overlapping Triangles

4-7

Practice (continued)

Form G

14. Complete the following proof.

Given: , ÐRUT and ÐUTS are right angles, V is the midpoint of US.

Prove: RVU @ TVS

Statements Reasons

1) , ÐRUT and ÐUTS are right angles, V is the midpoint of . / 1)
2) / 2)
3) / 3) All right angles are congruent
4) / 4) SAS
5) ÐRUS and ÐSUT are complementary angles. / 5)
6) / 6) Definition of complementary angles
7) ÐSUT @ ÐRTU / 7)
8) ÐRUS @ ÐSTR / 8)
9) / 9) Definition of midpoint
10) ÐRVU @ ÐTVS / 10)
11) RVU @ TVS / 11)

15. Write a paragraph proof.

Given: P is the midpoint of

Prove: MRQ @ MRN

16. In the diagram at the right, ÐA @ ÐC, , and . Which two triangles are congruent by SAS? Explain.

Prentice Hall Gold Geometry • Teaching Resources