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Name:_______________________________________________________________
Date:_______________________
Period:_______
Chapter 5: Triangle Congruency Proofs
Topic 4: Isosceles Triangle Proofs
Vocabulary:
An ____________________ ___________________ is a triangle in which _____________ ___________________ are
____________________. In addition, the two base angles are also ____________________.
Using Isosceles Triangle in Proofs
To know that a triangle is isosceles, we can be ‘told’ many ways:



Given an isosceles triangle:
Given congruent sides:
Given congruent base angles:
or
Since all three of these things apply to isosceles triangles, any of those statements would let us know that we
have an isosceles triangle. We can then make further conclusions:



…
…We then also know congruent sides:
Statement
Reason
…We then also know congruent angles:
Statement
Reason
…
…We then also know congruent angles:
Statement
Reason
…
…We then also know congruent sides:
Statement
Reason
Name:_______________________________________________________________
Examples:
1.) Given:
Prove:
is isosceles with <R as the vertex.
Date:_______________________
Period:_______
Name:_______________________________________________________________
Date:_______________________
Period:_______
Let’s Recall:
Let's think back to the first lesson of this chapter. We discussed that when triangles are congruent, then their
corresponding parts (angles and sides) are congruent. This can be abbreviated by ______________.
Sometimes in proofs, we are not asked to find two triangles congruent, instead we are asked to prove
something where we need to find their parts congruent. We can do this by using _________________.
If we are asked to prove ____________________or ____________________ are congruent:
1.) First prove the triangles containing these parts are congruent.
2.) Then state that the angles or sides are congruent by using the reasoning of ______________.
2.) Given:
Prove: a.)
b.)
is isosceles
Name:_______________________________________________________________
3.) Given:
bisects <ACB
Prove:
is isosceles
Date:_______________________
Period:_______
Name:_______________________________________________________________
Date:_______________________
Topic 4 Homework: Isosceles Triangle Proofs
1.) Given:
is altitude in
D is the midpoint of
Prove:
.
.
is isosceles.
2.) Given: ΔVIN is isosceles with vertex <I
is the median to
Prove:
Period:_______
Name:_______________________________________________________________
Date:_______________________
3.) Using the diagram below, find the m<Q.
Review Questions:
4.) Which diagram shows the construction of the perpendicular bisector of
?
5.) Using the given diagram, find the measure of <a. Explain how you arrived at your answer.
Period:_______
Name:_______________________________________________________________
Date:_______________________
Period:_______
6.) The point (3,-2) is rotated 90o about the origin and then dilated by a scale factor of 4. What are the
coordinates of the resulting image?
(1) (-12,8)
7.) In the diagram below of
an isosceles triangle with
(2) (12, -8)
, B is a point on
. Find m<C.
(3) (8,12)
such that
(4) (-8,-12)
is an equilateral triangle, and
8.) Find the slope of a line perpendicular to the line whose equation is 2y – 6x = 4.
9.) Construct a 30o angle on a separate sheet of paper. Show all construction marks.
is