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# TIU CET Review Math Session 3 Geometry by Young Einstein

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College Entrance Test Review
Math Session 3 Geometry
Points, Lines, Planes, Angles
Exercises on: Area, Perimeter, Circumference, Volume

Published in: Education, Technology
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### TIU CET Review Math Session 3 Geometry by Young Einstein

1. 1. GEOMETRY
2. 2. The 3 undefined terms in geometry • POINT
3. 3. • LINE
4. 4. • PLANE
5. 5. Exercises - Answers• Name a point. T, E, L, U, S, Y, or Z• Name three points that are collinear. T-L-S, or E-L-U, or Y-L-Z• Name three points that are non-coplanar. T- L-Z, T-L-Y, S-L-Y, others.• Name two rays. Ray LY, others. P• Name two coplanar lines. Line TS and T Eline EU. Y L7. Name two non-coplanar lines. Z Line YZ and line EU. U S
6. 6. 7. If line YZ is perpendicular to line TS, does it mean it is also perpendicular to line EU? YES.• Why or why not?
7. 7. 8. Name two pairs of adjacent angles. • Pair 1:∠bac and ∠cad • Pair 2: ∠dae and ∠eaf 9. Based on the figure on the left, give an example of: c d • Acute angle:b e ∠eaf , others • Obtuse angle: a ∠dae , others f
8. 8. 10. Complementary Angles 10. (a.) What is the complement of 40o? • COMPLEMENTARY ANGLES • - Two angles whose sum is 90o. • Answer to 10.(a.): = 90° − 40° = 50° 10.(b.) What is the complement of ( 14 − y ) °? = 90° − ( 14 − y ) ° = 90° − 14 + y = ( 76 + y ) °
9. 9. 11. Supplementary Angles• 11.(a.) Find the supplement of 78.6°• Supplement: = 180° − 78.6° = 101.4°• SUPPLEMENTARY ANGLES• - Angles whose sum is 180o.11.(b.) Find the supplement of ( x + 56 ) ° = 180° − ( x + 56 ) ° = 180° − x − 56° = ( 124 − x ) °
10. 10. 12. Solve for x. 5xo 2xo • One full revolution 3x o is 360o. 2 x + 5x + 3x + 90 = 360 10 x + 90 = 360 10 x = 270 x = 27°
11. 11. 13. Calculate the values of y and z. • 2y and 7x are 2y o VERTICAL ANGLES. 7x o  Formed when two lines intersect. 140o • 2y = 7xPCA Theorem:Given two lines Parallel, the Corresponding Anglesare congruent. 140 = 7x
12. 12. 2y = 7 x140 = 7 x 2y = 7 ( 20 )140 7 x = 2y = 140 7 7 20 = x 2y 140 = 2 2 y = 70
13. 13. 13. (b.) Solve for y and z. • Angle y and 316 make one cycle.  y + 316 = 360 • So, y = 44o. • PAI Theorem: z • Given parallel lines, the Alternate Interior Angles 58 are congruent.  z = 58o
14. 14. 14. The ratio of the angles of a triangle is 2 : 5 : 8. What are the measures of the angles of the triangle?• What is the sum of the measures of the angles of a triangle?• 180o• How do we calculate proportion? 15 squares •2 : 5 : 8
15. 15. • If the sum of the 3 angles was 15 degrees, then the measures would be 2°,5°, and 8.°• 2 : 5 : 8  15 15 × ? = 180 ? = 12 24 : ____ : _____  180•___ 60 96• Therefore , the angle measures are 24, 60, and 96 degrees.
16. 16. 15. What is the value of x?• CONCEPT:The sum of the measures of the angles of a triangle is 180 degrees.
17. 17. 16. If the three angles of a quadrilateral were: y, ( 50 + y ), ( y – 75 ), what is the fourth angle? CONCEPT: The sum of the measures of the angles of a quadrilateral is 360 degrees.
18. 18. 17. In a parallelogram PQRS, ∠QPR = 56° and ∠QRS = 70°. Calculate . ∠RQP ________ and∠PRQ _________.• PARALLELOGRAM - A quadrilateral with 2 pairs of opposite sides parallel.• Drawings: Be careful in labeling.
19. 19. Q R 110° 14° 110° ∠RQP ________ 70° Adjacent angles of a parallelogram are 56° SUPPLEMENTARY. 14° ∠PRQ _________P S ∠PRQ = 180 − ( 56 + 110 ) = 180 − 166 = 14°
20. 20. 18. In the figure below, x = 60 deg. Howmuch more is the perimeter of the triangleDEF compared to that of triangle ABC?
21. 21. 19. Square ABCD is inscribed in a circle.The square has a side of length 6cm. What is the area of the shaded region? • Area of a circle A =πr 2 • Area of a square A = side = s 2 2 • Pythagorean Theorem a +b =c 2 2 2
22. 22. 20. Daniel has a square piece of paper of side 4 inches. If he rolls up the paper tomake a cylinder, what is the volume of the cylinder formed?
23. 23. 21. A rectangle and a triangle share thesame base. If the area of the triangle is 6times the area of the rectangle, and theheight of the rectangle is 4, what is theheight of the triangle?
24. 24. 22. In the figure on the right, BCDE is asquare and AB = 12. What is the area ofsquare BCDE? • 30-60-90 Theorem »What is the measure of side BE?
25. 25. 23. How many circles of radius10cm can be cut from arectangular board 1.2m by 0.8m?