G.CO.C.10 Guide 1

​To prove the triangle angle sum theorem with a two-column proof, we need an auxiliary line.

​Do this on page 162.

​?

​What do we know about the measures of angles 4, 2 and 5, if they were added together?

​The measure of a straight line is 180 degrees

Multiple Choice

What property says if I know a = b, then I can replace a with b anywhere in the problem?

• reflexive property

• commutative property

• substitution property

• addition property

​The measure of a straight line is 180 degrees

​substitution property of equality

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The three angles of a triangle add up to

degrees.

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$m\angle C=$  

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$m\angle B=$  

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$m\angle A=$  

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$m\angle A=$  

​What is an isosceles triangle?

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​What is an isosceles triangle?

​

​Leg

​Leg

​Vertex Angle

​Base Angle

​Base Angle

​Base

​The congruent sides are called legs.

​

The other side is called the base.​

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The angles that touch the base are called Base Angles.​

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The angle created by the legs is the vertex angle. ​

Multiple Choice

Which angle is the vertex angle?

• $$\angle C$$  

• $$\angle A$$  

• < $$\angle B$$  

Multiple Select

Which angle(s) is/are the base angle(s)? Select all that apply.

• $$\angle W$$  

• $$\angle X$$  

• $$\angle Y$$  

Multiple Choice

What side is the base?

• $$\overline{XY}$$  

• $$\overline{WX}$$  

• $$\overline{WY}$$  

​Line BD is an auxiliary line that is perpendicular to Side AC.

​

Prove the base angles are congruent.

​

This is on page 163.​

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​In an isosceles triangle, the following are always true.

1. The legs are congruent (definition of isosceles triangle).

2. The base angles are​ congruent (isosceles triangle theorem).

​

​If there are two congruent angles in a triangle, the triangle is an isosceles triangle and those two angles are the base angles.

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$m\angle C=$  

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$m\angle A=$  

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$m\angle C=$  

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$m\angle D=$  

​Triangle Exterior Angle Theorem

​

In a triangle, the measure of an exterior angle will be equal to the sum of the two remote interior angles.​

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$m\angle BCD=$  

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$m\angle B=$  

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$m\angle A=$  

​

​In a triangle, a midsegment is a segment that connects the midpoints of two sides of a triangle.

​Triangle Midsegment Theorem:

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A midsegment will be parallel to and half the length of the third side. ​

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x =

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x =

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x =