3.5/3.6 Overlapping Triangles & Types of Triangles

1. I can use overlapping triangles in proofs. I can name the various types of triangles and their parts. 3.5/3.6 Overlapping Triangles & Types of Triangles Day 5

2. Example 1 • Given: ∠OTR≅∠HRT, • Prove: N H O R T

3. Classifying Triangles by angles • Acute triangle – a triangle with 3 acute angles • Right triangle – a triangle with one right angle • Obtuse triangle – a triangle with one obtuse angle

4. Parts of a right triangle hypoteneuse leg leg

5. Naming Triangles by Sides Scalene triangle – a triangle with no congruent sides Isosceles triangle – a triangle with at least two congruent sides Equilateral triangle – a triangle with all sides congruent (for triangles we can also call this equiangular)

6. Parts of an isosceles triangle vertex angle leg leg base angle base angle base

7. Example 3 • Classify the following triangle as scalene, isosceles, or equilateral if the perimeter is 45. 4x+3 15 7x-6

8. Example 4 • Given: altitude to , bisects ∠RGP • Prove: △GRP is isosceles G R P I

9. Always, Sometimes, Never • A right triangle is isosceles. • An isosceles triangle is equilateral. • An equilateral triangle is isosceles. • A scalene triangle is isosceles. • An equilateral triangle is equiangular. • A right triangle has two right angles.