Triangles Review.

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Presentation transcript:

Triangles Review

Classify each triangle by sides and angles. Can you identify the type of triangles in each of the following photos? Classify each triangle by sides and angles.

It’s an ISOSCELES, ACUTE triangle.

It’s a SCALENE, ACUTE triangle.

It’s an ISOSCELES, RIGHT triangle.

It’s an ISOSCELES, OBTUSE triangle.

It’s an EQUILATERAL, EQUIANGULAR triangle.

Not possible!!!! 1. Right Isosceles 2. Right Equilateral Draw an example of the following triangles, if possible. Mark the diagrams appropriately. 1. Right Isosceles 2. Right Equilateral Not possible!!!! 3. Obtuse Scalene

Geometry Unit 5, Lessons 1 & 2 Isosceles Triangles Geometry Unit 5, Lessons 1 & 2

An isosceles triangle is a triangle with two congruent sides. The sides that are the same length are called legs. The other side is called the base. The angles on each end of the base are called base angles. The angle across from the base is called the vertex angle.

Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite them are congruent.

Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite them are congruent.

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Example 1 Find x. Solution: If two angles of a triangle are congruent, the sides opposite them are congruent. Set: 6x - 8 = 4x + 2 2x = 10 x = 5 Note: The side labeled 2x + 2 is a distracter and is not used in finding x.

Example 2 Find the measures of 1,  2,  3 and  4. Solution: If two sides of a triangle are congruent, the angles opposite them are congruent. So m<1 = m<2 and m<3 = 40 degrees. 180 - 50 = 130 180 - (40 + 40) = 100 m<1 = 65 degrees m <4 = 100 degrees m<2 = 65 degrees