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Name__________________________________
Geometry
Quiz 8 Review
____ T10 (A4): Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Find the equation of the line with the following info.
5
1. Through (3, -1), parallel to 𝑦 = − 𝑥 − 1
2
3
2. Through (1, 5), perpendicular to 𝑦 = − 4 𝑥 − 5
3. Determine if the lines are parallel, perpendicular, or neither. Include the slope of each line in your work.
-10x + 6y = 7
y = 5/3x – 4
_____ T7 (A2): Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the
square to find the center and radius of a circle given by an equation.
4. Write the equation of the
circle with center (1,-3) and
radius 4.
5. Write the equation of the circle
with center (2,3) and the point (-2,
6) is on the circle.
6. Find the center and radius of
the circle with the equation:
𝑥 2 + 𝑦 2 − 8𝑥 + 8𝑦 − 4 = 0
____ T8 (A3): Derive the equation of a parabola given a focus and directrix.
7. Find the equation of the parabola with a focus at (-4, 2) and directrix y = -4
y
x
1
8. y = 12(x -2) 2+1
9. 𝑦 = 𝑥 2 − 8𝑥 + 15
Opens: _______
Opens: ___________
Vertex: ______
Vertex: _________
Axis of Symmetry: ______
Axis of Symmetry: ____
p= ________
p = ____________
Focus: ___________
Focus: __________
Directrix: _________
Directrix: ________
y
y
x
x
______ T1 (A4) - I can solve problems with Central angles and arc measures
̂ if 𝑆𝑉
̅̅̅̅ 𝑎𝑛𝑑 𝑊𝑇
̅̅̅̅̅
10. Find the m𝑆𝑊
are diameters.
̂ (the
11. Find the measure of ACB
major arc) in circle P.
̂ measures 100⁰, find the measure of
12. 𝑆𝐷
̂ . Q is the center of the circle.
𝑅𝐸
____ T9 (A1): Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a
figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on
the circle centered at the origin and containing the point (0, 2). CCSS.MATH.CONTENT.HSG.GPE.B.4
13. Quadrilateral FISH has vertices at F (0, -1), I (6, 1), S (8, 7) and H (2, 5). Prove it is a parallelogram.
Evidence:
̅̅̅
𝐹𝐼
̅
𝐼𝑆
̅̅̅̅
𝑆𝐻
̅̅̅̅
𝐻𝐹
Slope
Distance
Reasoning:
What is it? ___________________________________________
I know this because: ________________________________________________________________________
T9 continued…
Determine all of the possible quadrilaterals that could exist based on the properties.
14. I have opposite sides
congruent, opposite angles
congruent, and perpendicular
diagonals. What could I be?
15. I have one pair of
parallel sides. What could
I be?
16. I have adjacent
congruent sides. What
could I be?
Determine the most specific name you can apply to a quadrilateral with the following traits.
17. I have congruent diagonals
and 2 pairs of opposite sides that
are congruent.
18. I have 4 congruent
sides and 4 congruent
angles.
Find the values of the variables.
20. In the parallelogram below,
find x, y, and z.
22. Find x and y that prove this is a parallelogram.
21.
19. I have perpendicular
diagonals and 4 congruent
sides.