Prove the Following:

Question

Given: BR = PA, ∠IAB ≅ ∠NBP, IR ⊥ IA, and NP ⊥ NB

Prove: IR = NP

Answer 1

Proof Reason

(1) BR+RP =PA+RP Addition Property of equality.

(2) BP = AR Segment Addition Postulate.

(3) m∠AIR=m∠BNP=90° Perpendicular lines form a right angle and measures 90°.

(4) ∠AIR≅∠BNP All right angles are congruent.

(5) ΔAIR ≅ΔBNP AAS Theorem of Congruent Triangles.

(6) IR = NP Corresponding Parts of Congruent Triangles are Congruent. (CPCTC)

Answer 2

right triangles RIB and PNA are congruent

BECUASE...

1) angles NPA = angle IRB = 90 are both right

angles, per the given perpendicular NP perpendicular to NB

and IR perpendicular to IA

2) BR = PA is given

3) since angles IAB = angle NBP, IA is parallel to BN.

This forces angle IBR = angle NAP