Unit 5: Relationships in Triangles

Unit 5 Learning Targets 

LT 5-1: I can use a perpendicular bisector to find missing measures.

LT 5-2: I can use an angle bisector to find missing measures.

LT 5-3: I can use medians and altitudes to find missing measures.

LT 5-4: I can apply the triangle inequality conjecture.

LT 5-5: I can use the triangle inequality to compare triangles.

LESSON 5-1

Perpendicular and Angle Bisectors

The perpendicular bisector of a segment contains all the points that are equidistant from the endpoints of the segment, and an angle bisector contains all the points that are equidistant from the sides of the angle.

Help Videos:

●       How Do You Construct a Perpendicular Bisector?

●       How Can You Tell If a Point Is on the Perpendicular Bisector of a Line Segment?

Practice:

5-1 Math XL

LESSON 5-2

Bisectors in Triangles

The perpendicular bisectors of the sides of a triangle are concurrent at its circumcenter. The angle bisectors of a triangle are concurrent at its incenter.

Help Videos:

●       What Is the Incenter of a Triangle?

●       What Is the Circumcenter of a Triangle?

Practice:

5-2 Math XL

LESSON 5-3

Medians and Altitudes

The medians of a triangle are concurrent at its centroid. The lines containing the altitudes of a triangle are concurrent at its orthocenter.

Help Videos:

●       What Is a Median of a Triangle?

●       How Do You Use the Centroid to Find Segment Lengths in a Triangle?

Practice:

5-3 Math XL

LESSON 5-4

Inequalities in One Triangle

The lengths of the sides of a triangle are related to the measures of the angles in the triangle. The sum of the lengths of two sides of a triangle is greater than the length of the third side.

Help Videos:

●       How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?

●       How Do You Put the Sides of a Triangle in Order According to Size If You Know Two Angles of the Triangle?

Practice:

5-4 Math XL

LESSON 5-5

Inequalities in Two Triangles

When two triangles have two pairs of congruent sides, the longer third side is opposite the larger included angle and the shorter third side is opposite the smaller included angle.

Help Videos:

●       What Is the Hinge Theorem?

●       How Do You Use the Hinge Theorem to Compare Side Lengths in Two Triangles?

Practice:

5-5 Math XL

Unit 5 Vocabulary

●       equidistant 

●       circumcenter of a triangle

●       circumscribed about

●       concurrent lines

●       incenter of a triangle

●       inscribed in

●       point of concurrency

●       altitude of a triangle

●       centroid of a triangle

●       median of a triangle

●       orthocenter of a triangle