Question

In ∆ABC shown below, ∡BAC is congruent to ∡BCA.
Triangle ABC, where angles A and C are congruent


Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that Line segment AB is congruent to Line segment BC making ∆ABC an isosceles triangle.
Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the _______1________.
Line segment AD is congruent to Line segment DC by _______2________.
∆BAD is congruent to ∆BCD by the Angle-Side-Angle (ASA) Postulate.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

1. the definition of congruent angles
2. Angle-Side-Angle (ASA) Postulate

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

1. Angle-Side-Angle (ASA) Postulate
2. the definition of a perpendicular bisector

1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)

Answer 1

What's your question?

Answer 2

its pretty much finding 1 and 2 in the paragraph thingy.

Answer 3

@NaCl Help?

Answer 4

Someone help?

Answer 5

Okie dokie, what does the A-S-A postulate say? And what does it mean for 2 angles to be congruent?

Answer 6

two angles are congruent?