Question

u2 lesson 6/7: isosceles triangle and side - angle - side

• create a angle bisector of angle p, name the other end point j

isosceles triangle:
angle bisector:
reflexive property:

• prove △bpj≅△apj

statement	reason
∠____≅∠____
pj≅pj	reflexive property
	side - angle - side congruence theorem (sas)

isosceles triangle theorem: in an isosceles triangle, the base angles are congruent.
ap = pb so ∠a=∠b

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle $\triangle PAB$, the two equal - sides are $PA\cong PB$ by the definition of an isosceles triangle.

Step2: Recall angle - bisector property

Since $PJ$ is the angle - bisector of $\angle P$, then $\angle BPJ\cong\angle APJ$.

Step3: Apply SAS congruence

We have $PA\cong PB$, $\angle BPJ\cong\angle APJ$, and $PJ\cong PJ$ (reflexive property). By the Side - Angle - Side (SAS) congruence theorem, $\triangle BPJ\cong\triangle APJ$.

Answer:

Statement	Reason
$\angle BPJ\cong\angle APJ$	Definition of angle bisector
$PJ\cong PJ$	Reflexive property
$\triangle BPJ\cong\triangle APJ$	Side - Angle - Side congruence Theorem (SAS)