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Warm UP March 10, 2014 Classify each triangle by its angles and by its sides.

E. C. 60°. 45 °. 60°. 60°. 45°. B. G. A. F. Warm UP March 10, 2014 Classify each triangle by its angles and by its sides. EOCT Week 9 #1. Parts of Isosceles Triangles. The angle formed by the congruent sides is called the vertex angle.

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Warm UP March 10, 2014 Classify each triangle by its angles and by its sides.

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  1. E C 60° 45° 60° 60° 45° B G A F Warm UP March 10, 2014Classify each triangle by its angles and by its sides.

  2. EOCT Week 9 #1

  3. Parts of Isosceles Triangles The angle formed by the congruent sides is called the vertex angle. The two angles formed by the base and one of the congruent sides are called base angles. The congruent sides are called legs. leg leg base angle base angle The side opposite the vertex is the base.

  4. Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. If , then

  5. Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. If , then

  6. EXAMPLE 1 Apply the Base Angles Theorem Find the measures of the angles. SOLUTION Q P Since a triangle has 180°, 180 – 30 = 150° for the other two angles. Since the opposite sides are congruent, angles Q and P must be congruent. 150/2 = 75° each. (30)° R

  7. EXAMPLE 2 Apply the Base Angles Theorem Find the measures of the angles. Q P (48)° R

  8. EXAMPLE 3 Apply the Base Angles Theorem Find the measures of the angles. Q P (62)° R

  9. EXAMPLE 4 Apply the Base Angles Theorem Find the value of x. Then find the measure of each angle. P SOLUTION (12x+20)° Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4 20 = 8x – 4 24 = 8x 3 = x (20x-4)° Q R Plugging back in, And since there must be 180 degrees in the triangle,

  10. EXAMPLE 5 Apply the Base Angles Theorem Find the value of x. Then find the measure of each angle. Q P (11x+8)° (5x+50)° R

  11. EXAMPLE 6 Apply the Base Angles Theorem Find the value of x. Then find the length of the labeled sides. SOLUTION Q P (80)° (80)° Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 7x = 3x + 40 4x = 40 x = 10 3x+40 7x Plugging back in, QR = 7(10)= 70 PR = 3(10) + 40 = 70 R

  12. EXAMPLE 7 Apply the Base Angles Theorem Find the value of x. Then find the length of the labeled sides. P (50)° 5x+3 (50)° R Q 10x – 2

  13. Right Triangles HYPOTENUSE LEG LEG

  14. Exterior Angles Interior Angles

  15. Triangle Sum Theorem The measures of the three interior angles in a triangle add up to be 180º. x + y + z = 180° x° y° z°

  16. R m R + m S + m T = 180º 54° 54º + 67º + m T = 180º 121º + m T = 180º 67° S T m T = 59º

  17. m  D + m DCE + m E = 180º E 55º + 85º + y = 180º B y° 140º + y = 180º C x° 85° y = 40º 55° D A

  18. Find the value of each variable. x° 43° x° 57° x = 50º

  19. Find the value of each variable. 55° 43° (6x – 7)° (40 + y)° 28° x = 22º y = 57º

  20. Find the value of each variable. 50° 53° x° 50° 62° x = 65º

  21. Exterior Angle Theorem The measure of the exterior angle is equal to the sum of two nonadjacent interior angles 1 m1+m2 =m3 2 3

  22. Ex. 1: Find x. B. A. 72 43 148 76 x x 38 81

  23. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. x + y = 90º x° y°

  24. Find mA and mB in right triangle ABC. mA + m B = 90 A 2x + 3x = 90 2x° 5x = 90 x = 18 3x° C B mA = 2x mB = 3x = 2(18) = 3(18) = 54 = 36

  25. Homework: Practice WS

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