The two triangles in the figure are congruent | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) In $	riangle OPQ$ and $	riangle OSR$,we are given $OQ = OR$.Also,$\angle POQ = \angle SOR$ because they are vertically opposite angles.To prove

Vedclass · Accepted Answer

$OP = OS$

Vedclass · Answer

(C) In $	riangle OPQ$ and $	riangle OSR$,we are given $OQ = OR$.Also,$\angle POQ = \angle SOR$ because they are vertically opposite angles.To prove the triangles are congruent by the $SAS$ (Side-Angle-Side) congruence criterion,we need another side adjacent to the angle $\angle POQ$ and $\angle SOR$ to be equal.The sides adjacent to the angles are $OP$ and $OQ$ in $	riangle OPQ$,and $OS$ and $OR$ in $	riangle OSR$.Since we already have $OQ = OR$,we need $OP = OS$ to satisfy the $SAS$ condition.Therefore,the condition $OP = OS$ is sufficient.

The two triangles in the figure are congruent using a congruence theorem. It is given that $OQ = OR$. Which of these conditions,along with the given condition,is sufficient to prove that the two triangles are congruent to each other?

Similar Questions

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB^2 + AC^2 = 338$ and $AD = 5$,find $BC$.

In rhombus $ABCD$,$AC = 12$ and $BD = 16$. Find the perimeter of rhombus $ABCD$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 18$,$AC = 14$,and $AD = 14$,find the perimeter of $\Delta ABC$.

The area of an equilateral triangle is $36 \sqrt{3}$. Find the measure of its sides.

In $\Delta ABC$,$m \angle A = m \angle B + m \angle C$. If $AB = 7$ and $BC = 25$,the perimeter of $\Delta ABC = ........$

Vedclass Test Series

Exam Paper Generator

Online Exam Module