Question

Given: pq = pr m∠qpr = m∠spk m∠q = m∠prk prove: ps = pk

Answer 1

To prove that ps = pk given pq = pr, m∠qpr = m∠spk, and m∠q = m∠prk, we use a proof by contradiction and the congruence of triangles.

Step-by-step explanation:

Proof:

Given: pq = pr, m∠qpr = m∠spk, and m∠q = m∠prk.

To prove: ps = pk

Proof by contradiction:

Assume that ps ≠ pk.

Since pq = pr, and m∠q = m∠prk, we can conclude that triangle pqk is congruent to triangle prk by the SAS (Side-Angle-Side) congruence theorem.

Therefore, ps must be equal to pk, contradicting our initial assumption.

Hence, ps = pk.