Download Honors Geometry MIDTERM REVIEW

Honors Geometry MIDTERM REIVEW
Transformations
1.
2.
3.
4.
5.
6.
7.
8.
Graph A(3, 2) B(2, 4) and C(1, 3) to form ΔABC.
Find the midpoint of every side of ΔABC.
How long is each side?
Draw each midsegment and state their lengths.
Translate ΔABC under the rule (x-4, y+2).
Rotate ΔABC 90° clockwise.
Reflect ΔABC over the x axis then the y-axis.
Does ΔABC have any line or rotational symmetry?
Equations of lines
Line a can be described by the equation y 
3
x  6.
5
9. Write an equation of a line that is parallel to line a?
10. Write an equation of a line that is perpendicular to line a?
Parallel Lines
Use the figure below to answer questions 11–14. Lines r and s are parallel.
11. State a pair of alternate interior angles? What is true about these angles?
12. State a pair of same-side interior angles? What is true about these angles?
13. Which of these explains why 4  8 ?
A vertical angles theorem
B alternate interior angles theorem
C
corresponding angles theorem
14. If m4 = (3y +1)°, m3 = 116° and m6 = (2x)°, write and solve equations to find x and y.
Congruent Triangles
15. Draw an example of each of the triangle congruency theorems.
SSS
SAS
AAS
ASA
HL
Use the figures below for 18–20. Given
16. What is mB ?
ABC 
PQR
17. What is PR?
18. By what theorem, postulate, or definition can you determine the angle and side measures for the figures
above? _______________________________________________________________________________
Triangles
19. Can you make a triangle with sides 5cm, 6cm and 11cm?
20. In ΔMID, MI=15cm, ID=18cm and MD=22cm. State the angles from smallest to largest.
For 21 & 22, use the figure.
21. If m1  53, what is m3?
22. Derrick states that
DEF is an isosceles triangle. Is Derrick correct? Explain.
Use ΔBCD for 23 & 24
23. Find the centroid for
BCD.
24. What lines would you need in
order to find the circumcenter?
25. Complete the proof to prove that
ABC 
CDA.
Statements
Reasons
1. ACD  ________
1.
2.
2. Given
3.
3.
4.
ABC 
CDA
4.
Explain why side BC would be congruent to side AD. _________________________
____________________________________________________________________
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
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24.
---(2.5,2) (1.5, 3.5) (2, 2.5)
AB = √5, AC = √5 CB = √2
---A’(-1, 4) B’(-2, 6) C’(-3, 5)
(y, -x) A’’(2, -3) B’’(4, -2) C’’(3,-1)
A’’’(-3, -2) B’’’(-2, -4) C’’’(-1, -3)
One line of symmetry – no rotation
y = 3/5x +/- and number
y = -5/3x +/- and number
Ex: 4 & 6 – congruent
Ex: 5 & 4 – supplementary
C
y = 21; x = 32
---92°
15
CPCTC
No
D, M, I
143°
No, since two angles are not congruent, then two sides are not congruent.
(-2, 2)
Perpendicular Bisectors
25.
Statements
1. ACD  CAB
1. Given
2. BCA  DAC
2. Given
3. AC  CA
3. Reflexive Property of Congruence
4.
1.
2.
3.
4.
5.
6.
7.
8.
Reasons
ABC 
CDA
4. ASA Triangle Congruence
Theorem
MPO
PRQ
112°
44°
Isosceles
19cm
120°
True – By the Isosceles Triangle Theorem, RQS = RSQ so RS = RQ