Question

Look at the figure below:

Which step should be used to prove that point P is equidistant from points R and Q?

If any one side and any one common angle are equal in triangles PQR and PRS, then their corresponding sides are also equal.

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

In triangles PQR and PQS, if one side and one angle are equal, then their corresponding sides and angles are also equal.

In triangles PRS and PQS, all three angles are equal.


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Answer 1

The correct option is

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

Explanation:

Given:

RS ≅ SQ

∠PSR ≅ ∠PSQ = 90°

To Prove:

point P is equidistant from points R and Q

i.e PR ≅ PQ

Proof:

In ΔPSR and Δ PSQ

PS ≅ PS ……….{Reflexive Property}

∠PSR ≅ ∠PSQ = 90° …………..{Measure of each angle is 90° given}

RS ≅ QS ……….{Given}

ΔPSR ≅ ΔPSQ ….{By Side-Angle-Side Congruence test}

∴ PR ≅ PQ .....{Corresponding Parts of Congruent Triangles}

i.e point P is equidistant from points R and Q .......Proved