University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2020
Views:

352

Pages:

3
Author:

StellarSymphony

Classifying Triangles Definition: A Triangle is a polygon with three sides. Angles sum to... 180° Classification: Triangles can be classified by their angle measures or by their side lengths. 1. Triangle Classification by Angle Measure a. Acute Triangle: ACUTE TRIANGLE QUESTIONS How many angles must be acute? All What do the angles have to measure? Must be less than 90° b. Equiangular Triangle: EQUIANGULAR TRIANGLE QUESTIONS What do all of the angles have to measure? 60° c. Right Triangle: RIGHT TRIANGLE QUESTIONS Could you have more than one right angle? No! What do we call the sides that form the right angle? Legs What is the name for the side opposite the right angle? Hypotenuse How would you classify the angles that are not right angles?1 Acute & Complementary 1. What is the famous theorem associated with right triangles? Pythagorean Theorem a² + b² = c² d. Obtuse Triangle: OBTUSE TRIANGLE QUESTIONS Could you have more than one obtuse angle? No! Example: Classify each triangle by its angle measures. a. △ADC... Rt. Triangle b. △ABD... Acute Triangle c. △BDC... Obtuse Triangle triangle with points A, B, C, and D labeled, with angles and side lengths marked Triangle Classification by Side Length a. Equilateral Triangle: Three congruent sides b. Isosceles Triangle: At least two congruent sides - How many congruent sides must an isosceles triangle have? At least 2 - What are the congruent sides of an isosceles triangle called? Legs - What is the name of the angle formed by the legs of an isosceles triangle? Vertex angle - What is the name of the side opposite the vertex angle? Base - What is the name for the angles formed by the base of the triangle? Base angles c. Scalene Triangle: No congruent sides Example: Classify each triangle by its side lengths. ΔHGF Scalene Triangle ΔHFE Isosceles Triangle ΔHGE Scalene Triangle NOTE: When we classify triangles, we classify by side length first, and then by angles. Tell whether the following are TRUE or FALSE: If a triangle is isosceles, then it is equilateral. False If a triangle is acute, then it has at least one acute angle. True A right triangle must have a right angle, and the other angles must be obtuse. False It is possible that a triangle may have two obtuse angles and one acute angle. False The longest side of a triangle is opposite the greatest angle. True If a triangle is equilateral, then it is isosceles. True A triangle can be scalene and acute. True The angles of a triangle must sum to 360 degrees. False The longest side of a right triangle is called the hypotenuse. True If two sides of a triangle are congruent, then the angles opposite those sides are congruent. True Could you have an isosceles right triangle? If so, what would the angles measure? 45°-45°-90° II. Using Triangle Classification Example: ... Find the side lengths of the triangle. Isosceles a. G /|\ / | \ / | 4x-10.7 K 2x+6.3 / | J_______|_______L 5x+2 4x+5 4x - 10.7 = 2x + 6.3 2x = 17 x = 8.5 b. G /|\ / | \ / | 3y-4 H 2y+3 / | F_______|_______H 5y-18 17 3y-4 = 2y+3 y = 7 2. A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel 1 1. 18 + 18 + 18 = 54 ft/beam 420 ft / 54 ft/beam = 7.778 only 7 can be made!