1.2 Angle Relationships and Similar Triangles

Vertical angles - have equal measure

Parallel Lines cut by a transversal form several special sets of angles

Alternate Interior Angles have equal measure

Alternate Exterior Angles have equal measure

Corresponding Angles have equal measure

Interior Angles on the same side of the transversal

have a sum of 180^o

Sum of Angles of any triangles is 180 ^o

Examples

Use the special relationships to find the measure of angles

1 = _______ 2 = _______ 3 = _______ 4 = _______

5 = _______ 6 = _______ 7 = _______ 8 = _______

Find the measures of the angles in the diagram below

If the measure of two angles of a triangle are 17 ^{o 41’} 13” and 96 ^o 12’ 10”, find the measure of the third angle.

Classify Triangles By Angle

Acute Triangles	Right Triangle	Obtuse Triangle
all angles are acute	one right angle	one obtuse angle

Classify Triangles By Sides

Equilateral Triangle	Isosceles Triangle	Scalene Triangle
All sides are equal	Two sides are equal	No sides are equal

Similar Triangles For triangle ABC to be similar to triangle DEF, the following conditions must hold.

1. Corresponding angles must have the same measure.

2. Corresponding sides must be proportional. The ratios of the corresponding sides must be equal

Similar Triangles versus Congruent Triangles

Equal angles equal angles and equal sides

Are two congruent triangles always similar?

Are two similar triangles always congruent?

Name Corresponding Angles in similar or congruent triangles:

Name Corresponding Sides in similar or congruent triangles

Example

Find the values of the sides labeled with variables in the pair of similar triangles.

Application

The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 p.m. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m. long. How tall is the lighthouse.