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POWER TEST—FIRST SEMESTER Geometry K. Santos Power Test Format (10 questions) Angles vertical angles—are congruent linear pair—are supplementary complementary angles—add to 90° supplementary angles—add to 180° perpendicular lines—form right angle Parallel lines corresponding angles—congruent alternate interior angles—congruent same-side interior angles—supplementary Triangles sum of the three angles is 180° exterior angles = sum of the 2 remote interior angles Angles—vertical angles (sample #8) Vertical angles are congruent 9x 126° 9x = 126° x = 14° Angles—vertical angles (sample #4) Vertical angles are congruent 3x – 15 2x + 13 3x – 15 = 2x + 13 x – 15 = 13 x = 28 Answer question asked---find the measure of an angle 3(28) – 15 = 69° or 2(28) + 13 = 69° Angles—Linear Pair (sample #3) Linear pair is supplementary (adds to 180°) 5x 5x + 4x – 27 = 180 9x – 27 = 180 9x = 207 x = 23 Answer question asked—find m<2 4(23) – 27 so m< 2 = 65° 4x - 27 Angles—complementary angles (not on sample but shows up on power tests) Complementary angles—add to 90° 3x 57° 3x + 57 = 90 3x = 33 x = 11 Angles—complementary ratio problem (sample #10) Complementary—angles add to 90° Two complementary angles are in the ratio of 1:4. 1:4 think 1x:4x So if complementary: 1x + 4x = 90 5x = 90 x = 18 Answer the question—find the larger angle 4x is larger than 1x 4(18) = 72° Angles—supplementary ratio problem (not on this power test) Supplementary angles—add to 180° Two supplementary angles are in the ratio of 2:3. Find the smaller angles 2:3 think 2x:3x Supplementary: 2x + 3x = 180 5x = 180 x = 36 Answer the question asked—find the smaller angle 2x smaller than 3x 2(36)= 72° Angles—supplement word problem (sample question #7) One angle is 20° less than its supplement. Find the angle. x: the angle 180 – x: its supplement One angle is 20° less than its supplement x = (180 – x) – 20 x = 180 – x - 20 x = 160 - x 2x = 160 x = 80 Remember, x was the angle, so the angle is 80° Angles—Complement word problem (not on this sample power test) One angle is 40° more than its complement. Find the angle. x: the angle 90 – x: its complement x = (90 – x) + 40 x = 90 – x + 40 x = 130 – x 2x = 130 x = 65° which is the angle So watch for complement or supplement watch of more than or less than Parallel Lines—corresponding angles (sample example #6) Corresponding angles---congruent 5x - 7 2x + 41 5x – 7 = 2x + 41 3x – 7 = 41 3x = 48 x = 16 Answer the question asked—find an angle 2(16) + 41 = 73° or 5(16) – 7 = 73° Parallel Lines—Alternate interior angles (no example on this power test) Alternate interior angles—congruent 6x - 10 4x + 18 6x – 10 = 4x + 18 2x – 10 = 18 2x = 28 x = 14 Parallel Lines—same side interior angles (example #1 on sample power test) Same side interior angles—supplementary (add to 180°) 2x 7x 2x + 7x = 180 9x = 180 x = 20 Triangles—interior angle sum (example #5) Triangle angle sum--180° 6x 2x 4x 2x + 4x + 6x = 180 12x = 180 x = 15 Be careful—sometimes they ask for a particular angle Triangles—exterior angle sum--numeric (example #2 on the sample power test) Exterior angle = sum of the 2 remote interior angles 62 x 112 = x + 62 50° = x 112 Triangles—exterior angle sum—algebraic (example #9 on sample power test) Exterior angle = sum of the 2 remote interior angles 4x 3x 154 154 = 3x + 4x 154 = 7x 22 = x Answer the question asked—measure of smaller angle (3x) 3(22) so the smaller angle measures 66°