Answer: 1.
Given: S is the midpoint of RT
PR=PT
To Prove: PRS=PTS
Step-by-step explanation:
If PR=PT in a triangle PRT, then the triangle is isosceles triangle.
Therefore, ∠PRT=∠PTR (opposite angles of an isosceles triangle are equal)
In ▲PRS and ▲PTS
PR=PT
∠PRT=∠PTR
PS=PS (PS is common)
therefore, ▲PRS≅▲PTS
Therefore, ∠PRS=∠PTS
Hence proved.
Answer: 2.
Given: E is the midpoint of AB and CD.
To Prove: AEC=BED
Step-by-step explanation:
If AB and CD are the diagonals of rectangle, then
diagonals AB=CD, sides AC=BD and AD=BC
In ▲AEC and ▲BED,
∠AEC=∠BED(vertically opposite angles)
AE=BE
AC=BD
therefore, ▲AEC≅▲BED
Therefore, ∠AEC=∠BED
Hence Proved.
