Perpendicular Lines, Parallel Lines and the Triangle Angle-Sum Theorem

2

Parallel Lines Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||.

DC

BA

In the above figure, the arrows show that line AB is parallel to line CD.With symbols we denote, .CDAB ||

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Theorem 3-7If a||b

and b||c

Then a||c

It 2 lines are parallel to the same line, then they are parallel to each other.

Lesson 2-3: Pairs of Lines 4

PERPENDICULAR LINES

Perpendicular lines are lines that intersect to form a right angle.

The symbol used for perpendicular lines is . 4 right angles are formed.

m

nIn this figure line m is perpendicular to line n.

With symbols we denote, m n

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Theorem 3-8If

and

Then

In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.

tm tn nm ||

3.3 Parallel Lines and the Triangle Angle-Sum Theorem Theorem 3-10 Triangle Angle-Sum Theorem

The angles in a triangle add up to 180°

Triangle Angle-Sum TheoremFind m<1.

35° 65°

1

Triangle Angle-Sum TheoremΔMNP is a right triangle. <M is a right angle and m<N

is 58°. Find m<P.

Using AlgebraFind the values of x, y, and z.

F J H

G39°

65° x°

21°

y° z°

Classifying TrianglesEquilateral: All sides congruent

Equiangular: All angles congruent

60° 60°

60°

Acute Triangle: All angles are less than 90°

Right Triangle: One angle is 90°

Obtuse Triangle: One angle is greater than 90°

Classifying TrianglesIsosceles: At least two sides congruent

Scalene: No sides congruent

Special CaseEquiangular Triangle = Equilateral Triangle

…and it’s also an Acute Triangle

60° 60°

60°

Classifying a TriangleClassify the triangle by its sides and angles.

Classifying a TriangleClassify the triangle by its sides and angles.

Using Exterior Angles of TrianglesExterior Angle of a Polygon

1 Exterior Angle

2 3

Remote Interior Angles

Theorem 3-11 Triangle Exterior Angle TheoremThe measure of the Exterior Angle is equal to the sum of the two Remote Interior Angles

m<1 = m<2 + m<3

Using the Exterior Angle TheoremFind the missing angle measure:

113°

30°170°

40°

45°

45°

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3