For #1 – 15: Which triangle congruence theorem proves these triangles congruent (SSS, SAS, ASA, AAS, or HL)? Write the congruence statements also.
1) 2) 3)
1) 2) 3)
4) 5) 6)
7) 8) 9)
10) 11) 12)
10) 11) 12)
13) 14) 15)
13) 14) 15)
For #16 – 21: Is the congruence statement true? If so, give the reason. If not, describe why not.
16) \(\triangle DBL\cong\triangle RYW\) 17) \(\triangle OAT\cong\triangle ORP\) 18)\(\triangle HPG\cong\triangle RTS\)
16) \(\triangle DBL\cong\triangle RYW\) 17) \(\triangle OAT\cong\triangle ORP\) 18)\(\triangle HPG\cong\triangle RTS\)
19) \(\triangle RAP\cong\triangle IDY\) 20) \(\triangle TEM\cong\triangle LEB\) 21)\(\triangle NSY\cong\triangle HST\)
For #22 – 27: To prove the triangles congruent by the given theorem or postulate, what other pairs of sides or angles would needed?
22) SAS 23) ASA 24) HL
22) SAS 23) ASA 24) HL
25)AAS 26) SSS 27) ASA
For #28 – 33: Can we prove these two triangles congruent? If yes, state the reasons for the three pairs used. If no, then describe a third pair of sides or angles needed to prove these triangles congruent.
28) 29) 30)
28) 29) 30)
31) 32) 33)
Statements |
Reasons |
1. \(\angle P\cong\angle R\) |
1. |
2. \(\angle RDE\cong\angle PED\) |
2. |
3. |
3. |
4. \(\triangle RDE\cong\triangle\) ______ |
4. |
We know \(\overline{WU}\cong\overline{IR}\) because _____________________________. Since \(\overline{WU}\perp\overline{WI}\) and \(\overline{WI}\perp\overline{IR}\) this means that \(\angle UWI\) and ______________ are both right angles, because ____________________________________________________ _____________________________________________. Since they are right angles, \(\angle UWI\cong\angle RIW\) because____________________________________. Finally, we can see that _________________ because of the________________ property. Therefore, \(\triangle UWI\cong\triangle RIW\) by _________________ .