Question

In ∆ABC shown below, ∡BAC is congruent to ∡BCA.


Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that is congruent to making ∆ABC an isosceles triangle.

Construct a perpendicular bisector from point B to .
Label the point of intersection between this perpendicular bisector and as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the definition of congruent angles.
is congruent to by by the definition of a perpendicular bisector.

Answer 1

In ∆ABC shown below, ∡BAC is congruent to ∡BCA.


Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that is congruent to making ∆ABC an isosceles triangle.

Construct a perpendicular bisector from point B to .
Label the point of intersection between this perpendicular bisector and as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the definition of congruent angles.
is congruent to by by the definition of a perpendicular bisector.

∆BAD is congruent to ∆BCD by the _______1________.
is congruent to because _______2________.
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector

1. the definition of a perpendicular bisector
2. the definition of congruent angles

1. the definition of congruent angles
2. the definition of a perpendicular bisector

1. the definition of congruent angles
2. corresponding parts of congruent triangles are congruent (CPCTC)

Answer 2

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/1001/1001_G3_Q1_a.gif

Answer 3

May someone please help me? And hello, all viewers! lol

Answer 4

geometry proofs :|
ok in general if 2 angles are congruent, then the 2 corresponding sides are congruent as well. Its called the Base Angle Theorem i believe


But specifically what they are looking for is to prove the 2 sides are same by showing 2 right triangles are congruent

AD is the perpendicular bisector
thus the 2 triangles are congruent by Angle-Side-Angle Postulate
then if 2 triangles are congruent, then all the sides are the same so AB = AC
and now you have shown triangle ABC is isosceles