Question

In the adjoining figure, if QR = SR and <PRQ = <PRS,
then show that
(a) trianglePRQ = trianglePRS
(b) PQ = PS​

Answer 1

Step-by-step explanation:

In ∆PRQ and ∆PRS

QR = SR ( Given)

<PRQ = <PRS (Given)

PR = PR (Common)

so,

∆PRQ and ∆PRS are congruatent triangle

then, ∆PRQ = ∆PRS and PQ = PS

Answer 2

Given that:

In the adjoining figure,

• QR = SR
• ∠PRQ = ∠PRS

Show that:

1. △ PRQ = △ PRS
2. PQ = PS

In △ PRQ and △ PRS:

Given,

• QR = SR
• ∠PRQ = ∠PRS

And,

• PR is common for both.

So,

• △ PRQ ≅ △ PRS (By SAS congruence rule)

And,

• PQ = PS (By CPCT)

Here,

• SAS = Side-Angle-Side
• CPCT = Corresponding Parts of Congruent Triangles