Question

Prove that, if the bisector of ZBAC of A ABC is perpendicular to side BC, then A ABC
is an isosceles triangle.
In figure 3.50, if seg PR = seg PQ,
show that seg PS > seg PQ.
Q
R
Fig. 3.50
E
In figure 3.51, in A ABC, seg AD
and seg BE are altitudes
and AE = BD
Prove that seg AD = seg BE
B.
Fig. 3.51
Let's learn.​

Answer 1

Step-by-step explanation:

In ΔADB and ΔADC

∠BAD=∠CAD (AD id the bisector of ∠BAC)

∠BAD=∠CDA=90

∘

(Given)

AD=DA (Common)

By ASA test of congruency

ΔADB≅ΔADC

∴∠B=∠C (corresponding angles of congruent triangles)

If two angles of a triangle are equal, then the triangle is said to be a isosceles triangle.