Question

PLEASE HELP! 100 points! I only have a few minutes.
Question 7 (1 point) In the diagram below BPPK and AP = PJ. B J A K What additional information is sufficient to prove APB AJPK by side-angle-side (SAS)? Ob Oc d 2 LA LK 21 22 21 LK LB LJ​

Answer 1

Answer:

The correct answer is B.

Angle 1 and Angle 2 are vertical angles.

Answer 2

Answer:

B. $\sf \angle 1 \cong \angle 2$

Step-by-step explanation:

The SAS Axiom, also known as the Side-Angle-Side axiom, is a fundamental principle in Euclidean geometry. It states that if two sides and the included angle of one triangle are congruent respectively to two sides and the included angle of another triangle, then the two triangles are congruent.

In other words, if two triangles have two sides that are equal in length and the included angle between these sides is equal, then the two triangles are congruent.

In this case:

$\sf \overline{BP} \cong \overline{PK}$ Given

$\sf \overline{AP} \cong \overline{PJ}$ Given

The remainig additional information, is the angle.

So

Here

$\sf \angle 1$ and $\angle 2$ are Vertically Opposite Angle and they are congruent.

So, the remaining additional information to prove $\sf \triangle APB \cong \triangle JPK$ by side-angle-side is:

B. $\sf \angle 1 \cong \angle 2$