4.1 apply triangle sum properties
- 1. 4.14.1 Apply Triangle Sum Properties Bell Thinger 1. 90º ANSWER right 2. 72º Classify each angle as acute, obtuse, or right. ANSWER acute 3. 116º ANSWER obtuse
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- 4. 4.1Example 1 SOLUTION The triangle has a pair of congruent sides, so it is isosceles. By measuring, the angles are 55°, 55°, and 70° . It is an acute isosceles triangle. Classify the triangular shape of the support beams in the diagram by its sides and by measuring its angles. Support Beams
- 5. 4.1Example 2 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 = y2 – y1( )2 x2 – x1( )2 + = 2 – 0( )2 (– 1 ) 0( )2 +– = 5 ≈ 2.2 OQ = y2 – y1( )2 x2 – x1( )2 + 2 = – 0( )6 0( )2 +– 3 = 45 ≈ 6.7
- 6. 4.1Example 2 PQ = y2 – y1( )2 x2 – x1( )2 + 3 – 2( )2 6( )2 +–= (– 1 ) = 50 ≈ 7.1 STEP 2 Check for right angles. The slope of OP is 2 – 0 – 2 – 0 = – 2. The slope of OQ is 3 – 0 6 – 0 = 2 1 . Therefore, PQO is a right scalene triangle. ANSWER 1 The product of the slopes is – 2 2 = – 1, so OP OQ and POQ is a right angle.
- 7. 4.1Guided Practice 1. Draw an obtuse isosceles triangle and an acute scalene triangle. obtuse isosceles triangle B A C acute scalene triangleP Q R SAMPLE ANSWER
- 8. 4.1 2. Triangle ABC has the vertices A(0, 0), B(3, 3), and C(–3, 3). Classify it by its sides. Then determine if it is a right triangle. isosceles; right triangle ANSWER Guided Practice
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- 10. 4.1 Find m JKM. Example 3 SOLUTION STEP 1 Write and solve an equation to find the value of x. Apply the Exterior Angle Theorem.(2x – 5)° = 70° + x° Solve for x.x = 75 The measure of JKM is 145°.ANSWER STEP 2 Substitute 75 for x in 2x – 5 to find m JKM. 2x – 5 = 2 75 – 5 = 145.
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- 12. 4.1 The tiled staircase shown forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other. Find the measure of each acute angle. Example 4 ARCHITECTURE SOLUTION First, sketch a diagram of the situation. Let the measure of the smaller acute angle be x°. Then the measure of the larger acute angle is 2x°. The Corollary to the Triangle Sum Theorem states that the acute angles of a right triangle are complementary.
- 13. 4.1Example 4 Use the corollary to set up and solve an equation. Corollary to the Triangle Sum Theoremx° + 2x° = 90° Solve for x.x = 30 So, the measures of the acute angles are 30° and 2(30°) = 60 . ANSWER
- 14. 4.1Guided Practice Find the measure of 1 in the diagram shown.3. The measure of 1 in the diagram is 65 .ANSWER
- 15. 4.1 4. Find the measure of each interior angle of ABC, where m A = x°, m B = 2x°, and m C = 3x°. m A = 30°, m B = 60°, m C = 90°ANSWER 5. Find the measures of the acute angles of the right triangle in the diagram shown. 26° and 64°ANSWER Guided Practice
- 16. 4.1Exit Slip 1. Find x. Then classify the triangle by its angles. 22; acuteANSWER 2. Find the measure of the exterior angle shown. 104°ANSWER
- 17. 4.1Exit Slip 3. Find x and y. 82, 58ANSWER
- 18. 4.1 Homework Pg 229-232 #14, 18, 32, 36, 40