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Level 2 - Princess

Area of focus: angles

Topics covered:

> Supplementary angles

> Complementary angles

> Congruent angles

> Adjacent angles

> Linear pairs

> Vertical angles

> Angle bisectors

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- 1. For the teacherʼs guide and all answersplease contact info@putterking.com Future KingsTM Education Program Subject: Math Level 2 (Princess)Putter King LLC All materials copyright © 2011Level 28 Shinagawa Intercity Tower A Putter King LLC2-15-1 Konan Minato-ku Tokyo, Japan All rights reserved 108-6028 Unit #: 2011010201
- 2. MathLevel 2 - Princess 2
- 3. SummaryArea of focus: anglesTopics covered: • Supplementary angles • Linear pairs • Complementary angles • Vertical angles • Congruent angles • Angle bisectors • Adjacent anglesSuggested time to complete (2 hrs): • Teaching material (40 minutes) • Practice activity (20 minutes) • Final project (60 minutes) 3
- 4. Supplementary AnglesSupplementary angles are two angles whose measures combined equal 180 degrees. 135° 140° α b 40° a Angle a and angle b (40° and 140°) are supplementary angles, because they add up to 180°. 45° θ Angle α and angle θ (135° and 45°) are also supplementary angles, even though they are not connected together, because they add up to 180°. 4
- 5. Complementary AnglesComplementary angles are two angles whose measures combined equal 90 degrees. 40° α 30° b 50° a Angle a and angle b (50° and 40°) are complementary angles, because they add up to 90°. 60° θ Angle α and angle θ (30° and 60°) are also complementary angles, even though they are not connected together, because they add up to 90°. 5
- 6. Congruent AnglesCongruent angles have the same angle (in degrees or radians). 135° θ α 135° Angle θ and angle α are congruent angles. Congruent angles do not have to point in the same direction, they only need to have the same angle rotation (in degrees or radians). 6
- 7. Adjacent AnglesTwo angles are adjacent if they have a common side and a common vertex. B C A D Angle BAC is adjacent to angle CAD because they have a common side (line AC) and they have a common vertex (point A) 7
- 8. Linear Pairs of AnglesTwo angles form a linear pair if and only if:• they are adjacent (have a common side) and• their other sides are opposite raysIn other words, a linear pair of angles is formed when two lines intersect. Twoangles are said to be linear pairs if they are both adjacent and supplementary. a b c d The following angles are linear pairs: • angles a and b • angles a and c • angles b and d • angles c and d 8
- 9. Vertical AnglesVertical angles are the angles opposite each other when two lines cross.In other words, vertical angles are a pair of non-adjacent angles formed bythe intersection of two straight lines. Vertical angles are always congruent, or of equal measure. a b c d The following angles are vertical angles: • angles a and d • angles c and b 9
- 10. Angle BisectorsAn angle bisector is a line or line segment that divides an angle into two equal parts. 35° 35° The two smaller angles are adjacent angles. 10
- 11. Practice Activity Find and correctly label the following: • pair of complementary angles (1) • pair of supplementary angles (3) • set of congruent angles (2) • pair of adjacent angles (2) • linear pairs of angles (2) • pair of vertical angles (2) • angle bisector (1) 11
- 12. Final ProjectRequirementsDesign and label a miniature golf hole that includes at least: • 2 pairs of complementary angles • 2 pairs of supplementary angles • 2 congruent angles • 2 pairs of adjacent angles • 1 linear pair of angles • 1 set of vertical anglesFor full points, be sure to: • draw and label at least one angle bisector (use a protractor to accurately draw the bisector) • use a protractor to accurately measure and label the rotation amount for 1 pair of complementary angles and 1 pair of supplementary angles • be creative! 12
- 13. Grading Rubric Bogey Par Birdie (70% - 79%) (80% - 89%) (90% - 100%) • Student included all required angles • Student did not include all • Student forgot to include a • Student correctly measured at required angles required angle least one bisector and twoAngles • Student incorrectly measured • Student incorrectly measured angles (one pair of more than one angle an angle complementary angles and one pair of supplementary angles) using a protractor • Student correctly labeled all angles • Student incorrectly labeled • Student incorrectly labeled an • Student correctly labeled at more than one angle angle least one bisectorLabels • Student incorrectly labeled the • Student incorrectly labeled the • Student correctly labeled the degrees of rotation for at least degrees of rotation for one degrees of rotation for at least one angle angle one pair of complementary angles and one pair of supplementary angles • Miniature golf hole design is • Miniature golf hole design is playable and aesthetically plain and simple • Miniature golf hole design is pleasing • Student lines and angles are playableDesign sloppy or incorrectly labeled • Student lines and angles are • Student lines and angles are neatly drawn and labeled • Miniature golf hole design neatly drawn and labeled • Miniature golf hole design is does not exhibit creativity creative and original 13

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