The answers to the power point questions from Friday’s power point are on the following slides. Copying these answers will not help you to develop the skills needed for this unit. It is necessary that you work through each problem and attempt to answer the questions BEFORE viewing the answers. These answers are intended to be a checkpoint for your skill development and should be used as such. REMEMBER, I can’t pour the knowledge into your brain nor can I magically give you the skills you need to be successful in Geometry. You have to struggle through and work to develop the skills.

You Try: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

(4x+6) (7x -12) Based on the definition of an angle bisector <JKM and <MKL are congruent angles. Therefore, 4x+6 = 7x – 12 6 = 3x -12 18 = 3x 6 = x <JKM = 4 x + 6 = 4(6) + 6 = 24 + 6 <JKM = 30 o (4x+6) o (7x -12) o

<4 + <5 = 180 <4 + <3 = 180 <5 + <1+ <2 = 180 < 3 + <1 + <2 = 180 <1 + <2 =< 4 <3 = < 5 <1 = <2 <1 = ½ ( <4) <2 = ½ ( < 4)

List all the pairs of supplementary angles List all the pairs of vertical angles

List all the pairs of supplementary angles <1 and <2 <2 and <4 <4and< 3 <3 and <1 <5 and< 6 <6 and <8 <8 and < 7 <7 and <5 List all the pairs of vertical angles

List all the pairs of vertical angles <2 and <3 <1 and < 4 <5 and <8 <6 and < 7

You Try: Solve for X. Then find the measures of the angles.

Solve for X. Then find the measures of the angles. You Try: Solve for X. Then find the measures of the angles. <ABC and < CBD are a linear pair so they are also supplementary. Therefore, 3x + 19 + 7x -9 = 180 10x + 10 = 180 10x = 170 x = 17 <ABC = 3x + 19 = 3(17) +19 = 51+19 = 70 <CBD = 7x – 9 = 7(17) – 9 = 119 – 9 = 110 o o

The following diagram shows an equilateral triangle The following diagram shows an equilateral triangle. Find the value of X and Z in degrees and explain your thinking.

The following diagram shows an equilateral triangle The following diagram shows an equilateral triangle. Find the value of X and Z in degrees and explain your thinking. X and 60 are vertical angles therefore x = 60 Because the triangle is equilateral, all angles of the triangle are 60 degrees. Z is also vertical angles to an angle of the triangle so it is also equal to 60 degrees

2x + 6 is vertical to 100 angle therefore, by the vertical angles theorem, 2x + 6 = 100 2x = 94 x = 47 2x + 6 = 2 ( 47) + 6 = 100 o o o o

The following diagram shows an isosceles triangle The following diagram shows an isosceles triangle. Find the value of x in degrees.

The following diagram shows an isosceles triangle The following diagram shows an isosceles triangle. Find the value of x in degrees. Base angles of an isosceles triangle, therefore the other base angle is 75 degrees. Angles that are a linear pair are supplementary, therefore the angle adjacent to the 75 degree angle must equal 105 degrees. The linear pair of the 105 degree angle and the angle labeled x + 20 must be supplementary so…. 105 + x + 20 = 180 x + 125 = 180 x = 55 105 75

By definition of vertical angles we know that 65 = y By definition of a linear pair, we know that X + 65 = 180 therefore x = 115 By definition of vertical angles we know that X = Z therefore we know that Z = 115.

Find the measure of each angle in degrees.

Find the measure of each angle in degrees c = 60 vertical angles congruent d = 30 c + d = 90 , 60 + d = 90 , d = 30 j= 90 vertical angles congruent n= 30 vertical angles congruent r= 30 vertical angles congruent g= 150 g + 30 = 180, g = 150 k= 150 vertical angles congruent