4 1 Classifying Triangles Triangles A polygon with

4. 1 – Classifying Triangles

Triangles • A polygon with three sides. • The corners are called vertices • A triangle with vertices A, B, and C is called “triangle ABC” or “

Classifying Triangles by Sides Scalene Triangle No congruent sides Isosceles Triangle Equilateral Triangle 3 congruent sides 2 congruent sides

Classifying Triangles by Angles Acute Triangle Obtuse Triangle All acute angles 1 obtuse angle Right Triangle Equiangular Triangle 1 right angle All congruent angles

Example 1: Classify triangles by sides and angles a) b) 7 c) 40° 15° 25 24 70° 120° Solutions: a) Scalene, Right b) Isosceles, Acute c) Scalene, Obtuse 45°

Example 2: Classify triangles by sides and angles Now you try… a) b) 5 5 5 3 4 5 c) 110°

Review: The distance formula To find the distance between two points in the coordinate plane…

EXAMPLE 3 Classify a triangle in a coordinate plane Classify PQO by its sides. Then determine if the triangle is a right triangle. SOLUTION STEP 1 Use the distance formula to find the side lengths. OP = = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 ( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 = OQ = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 = ( 6 – 0 )2 + ( 3 – 0 )2 = 5 2. 2 45 6. 7

EXAMPLE 3 Classify a triangle in a coordinate plane (continued) PQ = = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 ( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 = 50 7. 1 STEP 2 Check for right angles by checking the slopes. There is a right angle in the triangle if any of the slopes are perpendicular. 2– 0 The slope of OP is = – 2– 0 The slope of OQ is 3 – 0 = 1. 2 6– 0 so OP OQ and ANSWER Therefore, POQ is a right angle. PQO is a right scalene triangle.

Example 4: Classify a triangle in the coordinate plane Now you try… Classify ΔABC by its sides. Then determine if the triangle is a right triangle. The vertices are A(0, 0), B(3, 3) and C(-3, 3). Step 1: Plot the points in the coordinate plane.

Example 4: (continued) Classify a triangle in the coordinate plane Step 2: Use the distance formula to find the side lengths: AB = BC = CA = Therefore, ΔABC is a _______ triangle.

Example 4: (continued) Classify a triangle in the coordinate plane Step 3: Check for right angles by checking the slopes. The slope of = Therefore, ΔABC is a _______ triangle.