Study Guide Unit 5- Angles, Pythagorean Theorem, Transformations
SOL 8.6, 8.8, 8.10
Name: ______________________ Date: ______________ Block: _________
Define the following terms:
1) Adjacent Angles____________________________________________________________________________________________________
2) Complementary Angles___________________________________________________________________________________________
3) Supplementary Angles____________________________________________________________________________________________
4) Reflex Angles______________________________________________________________________________________________________
5) Vertical Angles ____________________________________________________________________________________________________
6) Pythagorean Theorem __________________________________________________________________________________________
7) Hypotenuse _____________________________________________________________________________________________________ _
Find the value of x in each figure.
8)
9)
For questions#10-11, use the picture to the right.
10) Angles ∠C and ∠B are ___________________________________ and _________________________________angles.
11) m∠C = ______________
m∠F = _______________
m∠E = ______________
12) Angles G and H are supplementary angles. If m G = 8x +3 and m
H = 105, find the value of x.
What is the measure of G? _________
Practice measuring and drawing angles. Use a protractor to complete 13a-c.
13)
a. Draw an acute angle. Label its measurement.
b. Draw a 128° angle.
c. Draw the reflexive angle of a 55° angle.
Pythagorean Theorem: Find the missing length to the nearest tenth.
14)
15) You built a 17 foot ladder for your treehouse.
The ladder needs to lean on the tree perfectly so
it reaches the front door. If the front door is 15
feet up the tree, how far away from the base of
the tree do you need to position the ladder?
16) Identify all sets of numbers which represent the measures of the sides of a right triangle.
a) 6, 8, 10
b) 9, 11, 14
c) 13, 14, 18
For questions #17-18, use the graph of JLM to the below.
17) Find the new coordinates of JLM after a 90° clockwise rotation. Draw the new figure.
J ____________
J’ ____________
L ____________
L’ ____________
M ____________
M’ ____________
J
M
L
18) What is the new coordinate of point L after JLM is translated 2 units horizontally and -3 units
vertically?
L ____________
L’ _____________
19) The vertices of ABC are A(3, 1), B(1, 4), and C(3, 4). Graph both the original and the image after a
rotation 180° about the origin. Identify coordinates of the new image.
ABC
A(3, 1)
B (1,4)
C (3,4)
A’B’C’
20) Reflect the image over the x-axis.
21) Measure the angle.
22) Identify which transformation is shown: translation, rotation, reflection, or dilation.
________________________________
23)
_______________________________
Measure the two angles that are not the right angle.
What can you say about the angles?
They are ____________________________
Verify:
_____________________________