Applying Triangle Sum Properties

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Presentation transcript:

Applying Triangle Sum Properties Lesson 4-1

Triangles Triangles are polygons with three sides.

Scalene Triangles Scalene triangles do not have any congruent sides. In other words, no side has the same length. 6cm 3cm 8cm

Isosceles Triangle A triangle with 2 congruent sides. 2 sides of the triangle will have the same length.

Equilateral Triangles All sides have the same length

Acute Triangle A triangle where all angles are acute angles.

Right Triangle A triangle with one right angle.

Obtuse Triangle A triangle with one obtuse angle.

Equiangular Triangles All angles have the same angle measure.

Classify by its SIDES

Classify by its ANGLES

Classify by its angles AND its sides

Obtuse Isosceles Right Scalene Acute Obtuse Right Equilateral Sketch an example of the type of triangle described. Mark the triangle to indicate what information is known. If no triangle can be drawn, write “not possible” Obtuse Isosceles Right Scalene Acute Obtuse Right Equilateral

Worksheet #1

Interior Angles vs. Exterior Angles Interior Angle: When the sides of a triangles are extended, the three original angles. Exterior Angles: When the sides of a triangles are extended, the angles that are adjacent to the interior angles.

Interior or Exterior?

Interior or Exterior?

Interior or Exterior?

Triangle Sum Theorem (Postulate Sheet) States that the sum of the interior angles is 180. 102° 56° 22°

Example Find the measure of each indicated angle. 98° 20° ? 54° 32° 53°

The sum of the angles is 180, so Example Find the value of x The sum of the angles is 180, so x + 3x + 56= 180 4x + 56= 180 4x = 124 x = 31

Example Find the measure of angle A 84° x +58° x + 52

Find the Value for X 2x + 15 3x 2x + 15 + 3x + 90 = 180 5x + 105 = 180

Corollary to the Triangle Sum Theorem (Postulate Sheet) Acute angles of a right triangle are complementary. 3x + 10 5x +16

Worksheet #2 (front)

Exterior Angle Sum Theorem The measure of the exterior angle of a triangle is equal to the sum of the non-adjacent interior angles of the triangle

88 + 70 = y 158 = y

2x + 40 = x + 72 2x = x + 32 x = 32

Find x and y 3x + 13 46o 8x - 1 2yo

Worksheet #2 (Back)