SOLUTION: Given: angle QPS is equal and congruent to angle TPR Prove: angle QPR is equal and congruent to angle TPS. The diagram has angle QPT divided into 3 smaller angles. Left: QPR

Algebra ->  Geometry-proofs -> SOLUTION: Given: angle QPS is equal and congruent to angle TPR Prove: angle QPR is equal and congruent to angle TPS. The diagram has angle QPT divided into 3 smaller angles. Left: QPR       Log On


   

Question 1181982: Given: angle QPS is equal and congruent to angle TPR
Prove: angle QPR is equal and congruent to angle TPS.
The diagram has angle QPT divided into 3 smaller angles.
Left: QPR
Interior: RPS
Right: SPT
The interior angle RPS is significantly larger than the 2 exterior angles QPR and SPT.

1.angle QPS =& congruent angle TPR. Given
2.m angle QPS = m angle TPR. Definition. of congruence
3.m angle QPS = m angle QPR + m angle RPS. Angle addition
m angle TPR = m angle TPS + m angle RPS. postulate
4. ____________________________. Substitution
5._______________________________. ________________
6. Angle QPR =&congruent to angle TPS. __________________
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the completed proof:
1. ∠QPS ≅ ∠TPR. Given
2. m∠QPS = m∠TPR. Definition of congruence
3. m∠QPS = m∠QPR + m∠RPS. Angle Addition Postulate
m∠TPR = m∠TPS + m∠RPS. Angle Addition Postulate
4. m∠QPR + m∠RPS = m∠TPS + m∠RPS. Substitution (Substituting step 2 into step 3)
5. m∠QPR = m∠TPS. Subtraction Property of Equality (Subtract m∠RPS from both sides)
6. ∠QPR ≅ ∠TPS. Definition of congruence