Unit 4 – Triangle Relationships

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Presentation transcript:

Unit 4 – Triangle Relationships Basic Facts, Characteristics, and Classifications

Activity - ANGLE SUMS IN TRIANGLES 1) Trace your triangle in the space below. Label the angles in your triangle. Choose one angle and extend the side to form an exterior angle. Example: 1 2 3 4

Activity - ANGLE SUMS IN TRIANGLES 2) Tear off the angles of the triangle not next to the exterior angle. Arrange them to fill in the exterior angle drawn. Label your exterior angle and your non-adjacent interior angles.

Activity - ANGLE SUMS IN TRIANGLES 3) Make a conjecture about the relationship between the measure of the exterior angle and the measure of the two nonadjacent interior angles. * A conjecture is an opinion or theory without sufficient evidence for proof. Applet on image

The sum of all the interior angles in a triangle = 180 Measure of the exterior angle = sum of the two interior non-adjacent angles The sum of all the interior angles in a triangle = 180 i. e. i. e.

PROOF: The sum of the measures of the angles of a triangle is 180. Given: Prove: Proof on p.94

Example 1: Use the diagram at the right to find the measure of .

On Your Own 1: Find the measure of the exterior angle shown at the right.

Example 2: Use the diagram at the right to find x.

On Your Own 2: Use the diagram at the right to find x.

CLASSIFYING TRIANGLES (SIDES) 2 3 Can an isosceles triangle be equilateral? Is it always? Sometimes No Can an equilateral triangle be isosceles? Is it always? YES YES

CLASSIFYING TRIANGLES (ANGLES)

Relationship of sides to interior angles in a triangle http://www.mathopenref.com/trianglesideangle.html

What are the degrees of each interior angle in any equiangular triangle? x x x Is the triangle also equilateral?

PROOF: The other 2 angles in any right triangle are complementary. Given: Any right Triangle Prove: The other two angles are complementary Statements Reasons A x y B C