Triangle A threesided polygon Sides and Triangle ABC
Triangle • A three-sided polygon. • Sides: , , and • Triangle ABC, written ABC. . • The vertices are point A, B, and C. • The angles are
Two ways to classify Triangles 1) Classify by Angles
1. If point Y is the midpoint of VX, and WY = 3. 0 units, classify ΔVWY as equilateral, isosceles, or scalene. Explain your reasoning. Since all three sides have different lengths, the triangle is scalene.
2. Find the measures of the sides __ of isosceles triangle KLM with base KL. Step 1 ML Find d. KM = 4 d – 13 12 – d = 5 d – 13 12 = 25 5 d d = =5 Step 2 Substitute to find the length of each side. KM = 4(5) – 13 = 7 ML KL = 5 + 6 = 12 - 5 = 11 =7
3. Find x and the length of each side if △RST is an equilateral triangle.
Classify each of the following triangles. 4. 5. 6. 8 8
Two ways to classify Triangles 2) Classify by Angles
Example: Find x and the length of each side if △RST is an equilateral triangle.
Classify the triangle as acute, equiangular, obtuse, or right. 9. 8. The triangle has three congruent angles. It is an equiangular triangle. One angle of the triangle measures 130°, so it is an obtuse angle. The triangle has an obtuse angle, so it is an obtuse triangle.
The frame of this window design is made up of many triangles. 10. Classify ΔACD. 11. Classify ΔADE. A. acute B. equiangular C. obtuse D. right
12. Classify ΔXYZ Answer: Since ΔXYZ has a right angle, it is a right triangle. 13. Classify ΔWXY Answer: Since ΔWXY has a right angle, it is a right triangle.
Triangle’s Angles Concept 22
Triangle’s Angles Cut out a triangle from a scratch piece of paper.
Triangle Sum Theorem A C B
Find the value of x for each. 4. 3. 8 x – 2 + 8 x – 2+ 7 x = 180 23 x - 4 = 180 3 x – 7 + 4 x + 6 + 90 = 180 7 x + 89 = 180 23 x = 184 7 x = 91 x=8 x = 13
2 x° (4 x + 12) ° 70°
9. Find the measure of the exterior angle shown. 10. Find the values of x and y. 13 x + 9 = 13(9) + 9 x + 75 = 3 x – 19 75 = 2 x – 19 94 = 2 x 47 = x 8 x + 3 + 51 = 13 x + 9 54 = 5 x + 9 45 = 5 x 9 =x = 126 + y = 180 y = 54
Find the measure of each numbered angle. 13. 14.
Find the measure of each angle. 3. m∠ 1 = 180 – 85 - 40 = 55 4. m∠ 2 = 55 5. m∠ 3 = 180 – 55 - 55 = 70
Find the measure of each angle. 15. m∠ 1 18. m∠ 4 = 60 + 80 = 140 16. m∠ 2 = 180 – 140 = 40 17. m∠ 3 = 105 – 40 = 65 = 180 – 105 = 75 19. m∠ 5 = 75 + 40 = 115
Find each measure. 5. m∠ 1 = 90 – 63 = 27 6. m∠ 2 = 90 – 63 = 27 90 – 27 = 63
7. GARDENING Find the measure of FLW in the fenced flower garden shown. m LOW + m OWL = m FLW Exterior Angle Theorem x + 32 = 2 x – 48 Substitution 32 = x – 48 each side. Subtract x from 80 =x Add 48 to each side. Answer: So, m FLW = 2(80) – 48 or 112.
11. Find m 3. A. 50 B. 45 C. 85 D. 130
12. Find the measure of each numbered angle. m 1 = 48 + 56 = 104 (90 – 34) + m 2 + m 4 = 180 104 + m 2 = 180 76 56 + 76 + m 4 = 180 132 + m 4 = 180 m 3 = 90 – 48 48 = 42 m 5 + 41 + 90 = 180 m 5 + 143 = 180 49
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