Use Isosceles and Equilateral Triangles

Use Isosceles and Equilateral Triangles

Geometry

Mrs. LaGrange

Micro-Presentations

Exploring Triangles

One slide in one minute or less.

Show what you already know!

Poll

Classify the triangle by its sides: 2cm, 2cm, 2cm

• equilateral

• isosceles

• scalene

Poll

Classify the triangle by its sides: 7ft, 11ft, 7ft

• equilateral

• isosceles

• scalene

Poll

Classify the triangle by its sides: 9m, 8m, 10m

• equilateral

• isosceles

• scalene

Math spoken here.

Vocabulary:

Legs: when an isosceles triangle has exactly two congruent sides, these sides are called legs.

Vertex angle: the angle formed by the legs.

Base: The third side of the isosceles triangle.

Base Angle: The two angles adjacent to the base.

Multiple Choice

Which segment is the base?

• Segment AB
• Segment BC
• Segment AC

Multiple Choice

Which angle is the vertex angle?

• <C
• <A
• <B

Theorems:

*Base Angles Theorem

*Converse of the Base Angles Theorem

Base Angles Theorem:

If two sides are congruent, then the angles opposite them are congruent.

Converse of the Base Angles Theorem:

If two angles are congruent, then the sides opposite them are congruent.

Multiple Choice

For isosceles triangles, when we are given that two sides are congruent we can prove that ______________________.

• two angles are congruent

• the third side is congruent

• three angles are congruent

• no other relationships exist

Multiple Select

 $In\ \Delta DEF,\ \overline{DE\ }\approx\overline{DF}.\$  Use the base angles theorem to choose the two congruent angles.

•  $\angle D$  

•  $\angle E$  

•  $\angle F$  

Multiple Choice

Complete the statement.

 $If\ \overline{HG}\approx\overline{HK},\ then\ \angle HGK\ \approx\angle\ldots$  

• GHK

• KGH

• HKG

• GKH

Multiple Choice

Complete the statement.  $If\ \angle KHJ\approx\angle KJH,\ then\ \overline{KH}\approx\ldots$  

•  $\overline{KH}$  

•  $\overline{KJ}$  

•  $\overline{JH}$  

Finding Measures: Angles

Isosceles Triangles

Triangle Sum Theorem: $m\angle J+m\angle H+m\angle I=180\degree\$ 
 $34\ +m\angle H\ +m\angle I\ =180$  
(Base Angles Theorem  $\angle H\approx\angle I$ )
 $34\ +2\ \left(m\angle H\right)=180$  
 $2\left(m\angle H\right)=146$  
 $m\angle H=73$  
v=73

Multiple Choice

Use the triangle sum theorem and the base angles theorem to find a.

• 45

• 50

• 80

• 25

Finding Measures: Legs

Isosceles Triangles

By the converse of the base angles theorem c = 14.

Multiple Choice

Find the measure of the missing side.

• 7

• 13

• 20

• 14.8

Corollaries

Recall:

Equilateral triangles are special cases of isosceles triangles that have three congruent sides.

Multiple Choice

 $Find\ m\angle P.$  

• 60

• 80

• 45

• 90

Challenge!

Find the value of x and y.

Multiple Choice

Find the value of x and y.

• x = 50, y = 1/2

• x = 1/2, y = 50

• x = 50, y = 2

• x = 2, y = 50

Closing:

1. If two sides of a triangle are congruent, then the angles opposite are also congruent. The converse is also true.
2. If a triangle is equilateral, then it is also equiangular.