UNIT 2 - RELATIONSHIPS IN GEOMETRY (ANGLES)

Date

Lesson Topic HW

Oct.3 2.1 Interior Angles in Triangles WS 2.1

Oct.5 2.2 Exterior Angles of a Triangle WS 2.2

Oct.10 2.3 Angles Involving Parallel Lines WS 2.3

Oct. 11 Mid-Chapter Review & EQAO Practice WS 2.MCR

Oct.12 2.4 Interior and Exterior Angles of Quadrilaterals WS 2.4

Oct.13 2.5 Interior and Exterior Angles of Polygons

(n – 2)180o

WS 2.5

Oct.16 2.6 Review for Unit 2 Test WS 2.6

Oct.18 2.7 UNIT 2 TEST

MFM 1P Lesson 2.1 Angles in a Triangle

The Sum of the Interior Angles in a Triangle (SIAT)

We can use this relationship to determine the third angle in a triangle when we know the other two angles or if we know one angle and the triangle is isosceles.

Ex. Find the measure of A in the triangle below.

We can use this relationship to determine the third angle in a triangle when we know the other two angles.

Ex. a) Write a relationship for the measures of the angles in isosceles DEF.

b) Use the relationship to determine the measures of D and F.

Ex. Triangles ABC and ACD are braces for the “Diner” sign. What are the values of a and b?

Classifying Triangles

-by side length Scalene Triangle – A triangle where all sides have a different length. Isosceles Triangle – A triangle where two sides have the same length. Equilateral Triangle – A triangle where all sides have the same length

– all angles are 60.

-by angle measure

Acute Triangle – A triangle in which all angles are less than 90.

Obtuse Triangle – A triangle which contains one obtuse angle. – an angle between 90 and 180

Right Triangle – A triangle in which one angle is 90.

Ex. Find all missing angles

WS 2.1

MFM 1P Lesson 2.2 Exterior Angles of a Triangle

Enrico is a carpenter. He is building a ramp. Enrico knows that the greater angle between the ramp and the ground is 160°. How can Enrico calculate the angle the vertical support makes with the ramp?

An exterior angle is formed outside a triangle when one

side is extended. GBC is an exterior angle of ABC.

We can use this relationship to calculate the measure of A.

Extend the sides of ABC to form the other exterior angles.

BAE = FBC =

The sum of the exterior angles of a triangle is:

This relationship is true for any triangle.

Ex. Determine the angle measure indicated by x.

WS 2.2

MFM 1P Lesson 2.3 Angles Involving Parallel Lines

Vertically Opposite Angles are the angles opposite each other when two lines intersect (cross). "Vertical" in this case means they share the same Vertex (or corner point), not the usual meaning of up-down.

Vertically opposite angles are equal.

In the diagram to the right, 1 = 3 and 2 = 4

When a transversal intersects two lines, four pairs of opposite angles are formed. The angles in each pair are equal. When the lines are parallel, angles in other pairs are also equal. We can use tracing paper to show these relationships.

Corresponding angles are equal. They have the same position with respect

to the transversal and the parallel lines.

Alternate angles are equal. They are between the parallel lines on opposite sides of the transversal.

Interior angles have a sum of 180°. They are between the parallel lines on the same side of the transversal.

We can use these relationships to determine the measures of other angles when one angle measure is known.

Two Angles are Supplementary if they add up to 180 Together they make a straight angle.

Angles on one side of a straight line will

always add to 180.

Two Angles are Complementary if they add up to 90 (a Right Angle).

Ex. Find the measures of all the unknown angles in the diagram below.

Ex. Determine the values of x and y.

Ex. Find the values of the unknown angles in each of the following.

a)

b)

c)

WS 2.3

MFM 1P Lesson 2.4 Interior and Exterior Angles of Quadrilaterals

Any quadrilateral can be divided into 2 triangles.

The sum of the angles in each triangle is 180°. The sum of the angles in 2 triangles is: 2 x 180° = 360°

At each vertex, an interior angle and an exterior angle form a straight angle. The sum of their measures is 180°.

A quadrilateral has 4 vertices. So, the sum of the interior and exterior angles is: 4 x 180° = 720° The sum of the interior angles is 360°. So, the sum of the exterior angles is: 720° - 360° = 360°

Ex. One angle of a parallelogram is 60°. Determine the measures of the other angles.

Ex. Find the value of the unknown angle.

Ex. Find the value of x and y.

WS 2.4

MFM 1P Lesson 2.5 Interior and Exterior Angles of Polygons

We can determine the sum of the interior angles of any polygon

by dividing it into triangles.

In each polygon, the number of triangles is always 2 less than the number of sides. So, the angle sum is 180° multiplied by 2 less than the number of sides.

We can write this as an equation.

Ex. Determine the sum of the interior angles in a 12-sided polygon.

Ex. A regular polygon has all sides equal and all angles equal. What is the measure of each interior angle in a

regular hexagon?

Ex. Determine the measure of one exterior angle for each regular polygon.

a) b)

Ex. Determine the angle measure indicated by each letter.

WS 2.5