Question

Given: line segment AB≅line segment BC

Prove: The base angles of an isosceles triangle are congruent.

The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent.


Statement Reason
1. segment BD is an angle bisector of ∠ABC. 1. by Construction
2. ∠ABD ≅ ∠CBD 2. Definition of an Angle Bisector
3. segment BD ≅ segment BD 3. Reflexive Property
4. 4. Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA 5. CPCTC


Which statement can be used to fill in the numbered blank space?
ΔDAB ≅ ΔDBC

ΔABD ≅ ΔABC

ΔABC ≅ ΔCBD

ΔABD ≅ ΔCBD

Answer 1

@phi

Answer 2

4. is the blank space, its kind of hard to read

Answer 3

i assume we have a picture like this

Answer 4

Yea

Answer 5

In geometry, we start with a few "assumptions" that are assumed true.
They are
(1) we can draw a line between any 2 points
(2) we can extend a line in either direction as far as we want
(3) a circle has a center and a radius (of some length)
(4) right angles are equal to each other
(5) parallel lines never meet

Answer 6

I see

Answer 7

those are pretty clear... except maybe the last one. But notice we don't say anything about triangles, or that there angles add up to 180... those things turn out to be true because of those 5 starting assumptions. If you think about it, that is amazing. 5 assumptions *force* triangles to have 3 angles that add up to 180 degrees.

Answer 8

but back to your problem

Answer 9

I see, I also appreciate the help

Answer 10

Given: line segment AB≅line segment BC

Prove: The base angles of an isosceles triangle are congruent.

to do this, we need a strategy. Luckily, we are given the steps that will work.

First step. Draw the angle bisector from pt B to the line segment AC