foundations of mathematics 11 chapter 2- angles...

Name: ______________________ Date: _________________

Foundations of Mathematics 11

Chapter 2- Angles & Triangles Lesson #2 - Review of Triangle Properties Part 1 - Review of the Pythagorean Theorem

The Pythagorean Theorem States:

In any right triangle, the sum of the squares of the two shorter sides ( _________ ) is equal to the

square of the longest side ( _____________________ ).

If you know the lengths of two sides of a right triangle, you can use this formula to calculate the

length of the third side.

For each triangle below, determine the unknown length. Give the answers to the nearest tenth.

(a) (b)

Example 1

For each triangle, determine the length of the unknown side to the nearest tenth when

necessary.

(a) (b) (c)

Part 2 – Classifying Triangles Triangles are generally classified by the lengths of their sides or by the measures of their angles.

By Sides By Angles

Equilateral – all three sides equal Acute – three acute (________________ ) angles

Isosceles – two sides are equal Right – one right angle

Scalene – no sides equal Obtuse – one obtuse angle

Example 2

Classify each triangle in two ways, by its sides and angles.

(a) (b)

By sides: _________________ By sides: ___________________

By angles: ________________ By angles: ___________________

(c) (d)

By sides: ___________________ By sides: ___________________

By angles: ___________________ By angles: ___________________

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Part 3 – Angle Sum Theorem

No matter the size or the type of triangle, the three angles of a triangle add to ____________ .

Example 3

Find the measure of the unknown angle:

(a) (b)

R = ________ B = ________

(c) (d)

X = ________ M = ________

(e) (f)

A = ________ O = ________

T = ________ P = ________

(g) (h)

C

A

T

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a = ________ a = ________

b = ________ b = ________

c = ________ c = ________

d = ________ d = ________

e = ________ e = ________

f = ________ f = ________

Part 4 – Exterior Angle Theorem

An exterior angle of a triangle and its adjacent interior angle are supplementary.

Example 4

Calculate the missing angle measures.

(a)

What do you notice about the sum of the exterior angle and the sum of the angles on the opposite

side of the triangle?

(a)

(b)

Assignment Worksheet #2