Question

Prove OPR=QRP using a paragraph proof. (Write out the words for symbols. For example, write "Z" as "angle" and "x" as
"congruent to.")

Answer 1

Answer:

$\triangle OPR \cong \triangle QRP$ as per AAS congruence.

Step-by-step explanation:

We are given two triangles $\triangle OPR \ and\ \triangle QRP$.

Side OP is parallel to Side QR.

OP || QR

$\angle O = \angle Q$

To prove:

The two triangles are congruent i.e. $\triangle OPR \cong \triangle QRP$

Solution:

Let us have a look at the triangles:

$\triangle OPR \ and\ \triangle QRP$

1. Given that $\angle O = \angle Q$.

2. Side OP || RQ so, $\angle OPR = \angle QRP$ because they are the alternate angles of parallel sides. (Alternate angels are equal when a line cuts two parallel sides).

3. Side PR is common to both the sides i.e. PR = RP

Hence, by AAS congruence i.e. two angles and a side which is not between the two angles are same.

$\therefore \triangle OPR \cong \triangle QRP$ as per AAS congruence.