Date post: | 19-Jun-2015 |
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GEOMETRY
The 3 undefined terms in geometry
• POINT
• LINE
• PLANE
Exercises - Answers1. Name a point. T, E, L, U, S, Y, or Z2. Name three points that are collinear. T-L-S,
or E-L-U, or Y-L-Z3. Name three points that are non-coplanar. T-
L-Z, T-L-Y, S-L-Y, others.4. Name two rays. Ray LY, others.5. Name two coplanar lines. Line TS and line EU.6. Name two non-coplanar lines.
Line YZ and line EU.
P
E
L
S
U
T
Y
Z
7. If line YZ is perpendicular to line TS, does it mean it is also perpendicular
to line EU? YES.
• Why or why not?
8. Name two pairs of adjacent angles.• Pair 1: • Pair 2: 9. Based on the figure on the left, give an example of:• Acute angle:
• Obtuse angle:
f
e
d
c
b
a
and bac cad and dae eaf
, otherseaf
, othersdae
10. Complementary Angles10. (a.) What is the complement of 40o?• COMPLEMENTARY ANGLES• - Two angles whose sum is 90o.• Answer to 10.(a.):
10.(b.) What is the complement of ? 14 y
90 4050
90 14
90 14
76
y
y
y
11. Supplementary Angles• 11.(a.) Find the supplement of • Supplement:
• SUPPLEMENTARY ANGLES• - Angles whose sum is 180o.
11.(b.) Find the supplement of
78.6180 78.6101.4
56x
180 56
180 56
124
x
x
x
12. Solve for x.
• One full revolution is 360o.
2xo
3xo
5xo
2 5 3 90 360 10 90 360 10 270 27
x x xx
xx
13. Calculate the values of y and z.• 2y and 7x are
VERTICAL ANGLES. Formed when
two lines intersect.• 2y = 7x
7x o
2y o
140o
PCA Theorem:Given two lines Parallel, the Corresponding Angles are congruent. 140 = 7x
140 7140 7
7 7 20
xx
x
2 7
2 7 20
2 1402 1402 2
70
y x
y
yy
y
13. (b.) Solve for y and z.• Angle y and 316 make one cycle. y + 316 = 360• So, y = 44o.
• PAI Theorem:• Given parallel lines, the Alternate Interior
Angles are congruent. z = 58o
z
58
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?
• 2 : 5 : 815squares
• If the sum of the 3 angles was 15 degrees, then the measures would be
• 2 : 5 : 8 15
•___ : ____ : _____ 180• Therefore , the angle measures are 24, 60,
and 96 degrees.
2 ,5 , and 8.
15 ? 180 ? 12
24 60 96
15. What is the value of x?
• CONCEPT:The sum of the measures
of the angles of a triangle is 180 degrees.
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.
17. In a parallelogram PQRS, and . . Calculate
• PARALLELOGRAM- A quadrilateral with 2 pairs of opposite sides parallel.
• Drawings: Be careful in labeling.
56QPR 70QRS ________ and _________.RQP PRQ
Q R
P S
70
56
_________PRQ
110
180 56 110
180 16614
PRQ
________ RQP
Adjacent angles of a parallelogram are SUPPLEMENTARY.
14
110 14
18. In the figure below, x = 60 deg. How much more is the perimeter of the triangle DEF compared to that of triangle ABC?
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
• Area of a square
• Pythagorean Theorem
2A r2 2A side s
2 2 2a b c
20. Daniel has a square piece of paper of side 4 inches. If he rolls up the paper to
make a cylinder, what is the volume of the cylinder formed?
21. A rectangle and a triangle share the same base. If the area of the triangle is 6 times the area of the rectangle, and the height of the rectangle is 4, what is the height of the triangle?
22. In the figure on the right, BCDE is a square and AB = 12. What is the area of square BCDE?
• 30-60-90 Theorem
»What is the measure of side BE?
23. How many circles of radius 10cm can be cut from a rectangular board 1.2m by 0.8m?