Answer To: Geometry Final Honors Geometry XXXXXXXXXXName: _____________________________________ Semester 1...
Dr. Shikha Maheshwari answered on Jun 10 2021
Geometry Final
Semester 1 Final Exam Review
132°
x°
Honors Geometry Name:
Take Home Final
For numbers 1 – 4, use the diagram.
B
1. Name two pairs of numbered angles that are supplementary.
Sol . ( 1, 2) and ( 2, 3) .
2. Name two pairs of numbered angles that are complementary.
Sol . ( 3, 4) and ( 4, 5) .
3. Name a pair of numbered angles that are vertical.
Sol . ( 1, 3) .
4. How many angles have their vertex at D?
Sol . Three.
5. Find the value of x.
Sol. We know that the sum of the angles in a triangle is equal to 180
0
. Therefore, we have
132 180
132 2 180
2 180 132
2 48
24 .
x x
x
x
x
x
A
C
2
D
3 4
5
F
50°
x°
130°
6. Find the value of x.
Sol.
Let us draw a parallel line which divides x into two angles 1 and 2 .
1 2 x (1)
Since, we know interior angles are equal and the sum of supplementary angles is equal to 180
0
, we have
1 50 (2)
and
2 130 180 (3)
2 180 130
2 50 (4)
Now, from equation (1), we have
1 2
50 50
100 .
x
x
x
(Using eq (2) and eq (4))
7. The measure of the supplement of an angle exceeds three times the measure of the complement of the angle by 12. Find the
measure of half of the supplement.
Sol. Let the angle be x .
Therefore, its supplement angle be 180 x .
According to the question
180 3 90 12
180 270 3 12
180 282 3
3 282 180
2 102
51
x x
x x
x x
x x
x
x
Measure of half of the supplement
1
180
2
1
180 51
2
1
129
2
64.5 .
x
8. ABCD is a rectangle. Find the coordinates of P, the midpoint of AC.
Sol. Coordinate of P = midpoint of AC
1 1
18, 12
2 2
(9,6)
Therefore, the coordinates of P, the midpoint of AC = (9, 6).
9. The measure of the supplement of an angle is 82 more than five times the measure of the complement of the angle. Find the
measure of the complement.
Sol. Let the angle be x .
According to the question
180 5 90 82
180 450 5 82
180 532 3
5 532 180
4 352
88 .
x x
x x
x x
x x
x
x
10. Find the area of the rectangle whose vertices are (–6, 7), (–15, –2), (–6, –2), and (–15, 7).
Sol.
Consider the rectangle as ABCD with A= (−15, -2), B = (-6, -2), C = (−6, 7) and D = (−15, 7). Since the abscissa and ordinates of
y
A B(18, 12)
D C
. P
a
33° b
137°
137° 33°
d
e
rectangle ABCD are equal. So the rectangle ABCD is also a parallelogram.
Area of rectangle ABCD = Area of ∆ ABD + Area of ∆BCD
2 Area of ABD (The diagonal of parallelogram divides it into two triangles of equal area)
2 2 2 2
2 2 2 2
1
base( ) height( )
2
1
2 ( 15 6) ( 2 2) ( 15 15) ( 2 7)
2
( 9) (0) (0) ( 9)
81 81
9
2
9
81sq units.
AB AD
11. In this figure, lines a, b, c, d, e, and f intersect as shown.
Based on the angle measures, which pair of lines is parallel?
a) a and c
b) c...