4 17 18 unit 11 lesson 2 triangle inequalities.notebook 1 April 17, 2018 Mar 219:53 AM 4/17 Aim: Triangle inequality theorem Do now: Homework: TBA Mar 212:35 PM What makes a triangle? http://www.mathwarehouse.com/geometry/triangles/triangleinequalitytheorem ruleexplained.php Jan 410:17 PM Theorem 1: The sum of the lengths of two sides of a triangle is greater than the length of the third side. AC + CB > AB CB + AB > AC AB + AC > CB 5+3>7 3+7>5 7+5>3 A C B 5 3 7 Jan 410:20 PM In #’s 1‐6 tell whether the given lengths may be the measures of the sides of a triangle? 1) 3, 4, 5 2) 5, 8, 13 3) 6, 7, 10 4) 3, 9, 10 5) 2, 2, 3 6) 2, 4, 6 WRite these values next to the values there. Use these to values instead Jan 410:21 PM To calculate the range of the third side of a triangle you subtract the values and add the values, then write an inequality. 9, 5 9‐5= 9+5= < x< Jan 410:21 PM To calculate the range of the third side of a triangle you subtract the values and add the values, then write an inequality. < x< 14) 5, 8 15) 6, 10 16) 6, 9 17) 11, 8 18) 14, 11
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4 - 17 - 18 unit 11 lesson 2 triangle inequalities.notebook file4 17 18 unit 11 lesson 2 triangle inequalities.notebook 3 April 17, 2018 Jan 410:34 PM 2) Two sides of a triangle have
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2) Two sides of a triangle have lengths of 3 and 7. Find the range of possible lengths of the third side.
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3) Given the lengths of two sides of a triangle are a and b, can you use the Triangle Inequality Theorem to find a pattern for finding a possible length of the third side x.
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4) The length of the base of an isosceles triangle is 12. What can be said about the lengths of the legs of the triangle?
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5) If the lengths of two sides of a triangle are 4 and 13, the length of the third side can be what values?
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6) The lengths of two sides of an isosceles triangle are 9 and 15. Use an inequality to express the range of the length of the third side.
When the sides of triangle are not congruent, there is a relationship between the sides and the angles of the triangle.
• If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.• CONVERSE: If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Find the measure of an exterior angle at the baseof an isosceles triangle whose vertex angle measures400
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The vertex of an isosceles triangle measures eight timesthe measure of a base angle. Find the measure of the base angle. Find the measure of an exterior base angle.
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In triangle ABC, m<A = 50 and m<B = 20. Which is the longest side of the triangle?
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2. In triangle CDE, m<C = 70 and m<D = 60. Which is the shortest side of the triangle?
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3. In the accompanying diagram of triangle ABC, AC is extended to D. If m<BCD = 120 and m<B = 55,which is the longest side of the triangle?
DCA
B
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4. In triangle RST, the measure of angle R is 58 an exterior angle at S measures 118. Which is the longest side of the triangle?
14. In isosceles right triangle ABC, angle C is the right angle. Find the measure of the exterior angle at A.
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15. In ΔABC, AB = 5 feet and BC = 3 feet. Which inequality represents all possible values for the length of AC, in feet?1) 2 ≤ AC ≤ 82) 2 < AC < 83) 3 ≤ AC ≤ 74) 3 < AC < 7
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A
B
C D
12550
16. In the accompanying diagram of ΔABC, find in degrees, m<ABC.
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17. In ΔABC, m<C = 118 and m<B = 44. Which is the shortest side of the triangle?
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A B D
C
2x + 10
x + 30
4x + 30
18. In the accompanying diagram of ΔABC, side AB is extended to D. What is the value of x?
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19. In isosceles triangle ABC, AB = 10 and BC = 5. Which is the smallest angle of the triangle?