Download Geometry - pmaguire

Geometry
{
Semester 1 Review
2. Graph 2x + 3y = 6


There are two ways to do graph an equation that is listed in
STANDARD FORM.
1. Rearrange the equation into y-intercept form. In this case it
would be: y = -2/3 x + 2
2. Most efficient way to graph would be to find the x and y intercepts by
plugging in 0 for the x and solve for y, next repeat but plug in 0 for y and
solve for x. In this case 2(0)+3y=6, y=2 and
2x+3(0)=6, x = 3. Now just graph those points and connect the dots.
3. Write an equation that is perpendicular to
4x + 8y = -36 and passes through the point
(0, 7)

Step one is to find the slope of
our given equation.
4x + 8y = -36
-4x
-4x
8y = -4x – 36
8
8
8
y = -1/2 x – 4.5
Step three is to find the y-intercept.
In this case it is easy since (0,7) was
given to us and the y-intercept is the y
value when x = 0.
Step two is to find the slope of the
new equation. Remember that
parallel lines have the same slope
while perpendicular lines slopes are
opposite reciprocals. Therefore, the
slope of our new equation is +2
ANSWER:
y = 2x + 7
4. What is the value of x and y?
y = 52° (C-18) states that if a triangle
is isosceles, then the base angles are
congruent.
Finding x:
We know that the interior angles in
a triangle are 360°, therefore……
180 – 52 – 52 = 76
14x + 6 = 76
-6
-6
14x = 70
14 14
x=5
5. The coordinates of three vertices of a quadrilateral are shown
below. What would the ordered pair for the fourth vertex be to
make this quadrilateral a parallelogram?
(4,9)
Step 1: since a parallelogram has to
have two sets of parallel lines we
need to know the slope of one line.
(1, 5)
(5, 5)
9–5=4
4–1 =3
Slope = 4/3
Step 2: Plug our unknown (x,y) into the slope
equation and solve for them.
(x, y)
5–y=4
5–x=3
y = 1 and x = 2
ANSWER: (2, 1)
6. Line A is parallel to line B. What are the
values of x and y?
SOLUTION:
Step 1: Solve for x.
(12x – 42)° (12x – 42) and (8x + 14) are AIA and
therefore congruent.
(8x +14)°
(y – 3)°
STEP 2:
(8x + 14) and (y – 3) are vertical angles
which means they are congruent. Since we
know x = 14 ---- 8(14) + 14 = 126
y – 3 = 126
+ 3 +3
y = 129
12x – 42 = 8x + 14
+ 42
+42
12x = 8x + 56
-8x -8x
4x = 56
4
4
x = 14
7. What geometric relationship does the model
demonstrate.
ASA
8. What is the equation of the line graphed below?
y = 2x - 5
9. What are the coordinates of point B if (3, 8) is
the midpoint between points A (-2, 7)?

Remember the midpoint is an average of the x values and an average
of the y values since it is directly in the middle of the two endpoints.
X coordinate:
-2 + x = 3
2
Multiply both sides by 2
y coordinate:
7+y=8
2
-2 + x = 6
+2
+2
x=8
7 + y = 16
-7
-7
y=9
The coordinates of B are (8, 9)
10. In the figure, ray AE is parallel to ray DF, and
segment BD intersects AE at C. What is the measure of
angle BAC?

B
25°
135°
A
45°
E
C
45°
D
F
Since AE and DF are parallel
angle BCE corresponds to 45°
• Angle BCE (45°) is a linear pair with
Angle BCA therefore BCA = 180 – 45 =
135°
We now know two out of the
three angles in the triangle BAC.
<BAC = 180 – 135 – 25
<BAC = 20°
11. Which triangle congruence conjecture
(theorem) can be use in the figure below?
ASA
12.
a. List all congruent angles in the parallelogram below.
b. List all supplementary angles in the parallelogram.
<A ≅ <C and <B ≅ <D
<A + <D = 180°
<A + <B = 180°
<C + <D = 180°
<C + <B = 180°
13. What is the equation of the line that fits the data below?
x
y
-5
2
-3
3
-1
4
1
5
3
6
5
7
7
8
STEP 1:
Find the slope by rise/run or change in y/change in x
Slope = ½
STEP 2:
Find the y-intercept (y value when x = 0). Midpoint between 4 and 5
or choose a point from the table and use point – slope form to solve.
y – 5 = ½(x – 1) then simplify
y=½x+4½
14. Which quadrilaterals have the property,
diagonals are congruent?
Isosceles Trapezoid
Rectangle
Square
15. What are the coordinates of the
midpoint of the segment connecting the
points (-3, 8) and (11, -4)?

Remember; midpoints are just the average of
the x values and the average of the y values.
x – value:
y – value:
-3 + 11 =
2
8 + -4 =
2
8=
2
4=
2
4
2
(4, 2) = midpoint
16. An octagon has angle measures 100°,
85°, 130°, 155°. The remaining four angles
are congruent. What are the measures of the
remaining angles?
STEP 1:
Find the total sum of the interior angles using 180(n-2).
180(8 – 2) = 180(6) = 1080
STEP 2:
Subtract the known angle measures from 1080.
1080 – (100 + 85 + 130 + 155) =
1080 – 470 = 610
STEP 3:
Divide 610 by 4 since all four remaining angles are congruent.
610 ÷ 4 =
152.5°
17. Write an equation that represents a line that is parallel to the
line 4x – 2y = 16 and passes through the point (5, 9)
STEP 1:
Rearrange current equation from STANDARD form to Y-INTERCEPT form.
4x – 2y = 16
-4x
-4x
Parallel lines have the
-2y = -4x + 16
same slope; therefore, our
-2
-2 -2
new equation will have
the slope of 2.
y = 2x - 8
STEP 2:
Use POINT – SLOPE FORM
y –y1 = m(x – x1) m = 2, x1 = 5, y1 = 9
y – 9 = 2(x – 5)
y – 9 = 2x – 10
+9
+9
y = 2x -1