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 2 congruent sides Equilateral Triangle 3 congruent sides

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

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

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

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

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

EXAMPLE 3 Classify a triangle in a coordinate plane (continued) PQ= y 2 –y 1 ( ) 2 x 2 –x 1 ( ) 2 + 3– 2( ) 2 6 ( ) 2 + – = (– 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. The slope of OP is 2 – 0 – 2 – 0 = – 2. The slope of OQ is 3 – 0 6 – 0 = 2 1. so OP OQ and POQ is a right angle. Therefore, PQO is a right scalene triangle. ANSWER

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.