Download emsester 1 Test Review

Name:____________________________________Date:_____________Period:________
Semester 1 Geometry Review
Chapter 1 and 2:
1. Find the value of each variable:
a. .
b.
2. 𝑚∠𝐵𝐷𝐾 = 3𝑥 + 4 𝑎𝑛𝑑 𝑚∠𝐽𝐷𝑅 = 5𝑥 − 10 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚∠𝐾𝐷𝐽.
3.
Chapter 3:
4. What type of angle pair are angle 2 and angle 10.
5. If m∠7 + 𝑚∠6 = 180, which two lines are parallel, how do you know?
6. If 𝑛 ∥ 𝑝, 𝑚∠5 = 2𝑥 + 4, 𝑎𝑛𝑑 𝑚∠11 = 5𝑥 − 8. Find the value of x.
7. The angles in a triangle are in the ratio 2:3:4 find the angle measures.
8. Find the value of x:
Chapter 4:
9. Are the two triangles congruent? If so, how do you know? Write a congruence statement
if possible:
a.
b.
c.
10. Find the value of x:
11. Given: ̅̅̅̅
𝐾𝐿 ≅ ̅̅̅̅̅
𝑀𝑁 𝑎𝑛𝑑 ̅̅̅̅
𝐾𝐿 ∥ ̅̅̅̅̅
𝑀𝑁
Prove: ̅̅̅̅̅
𝐾𝑁 ≅ ̅̅̅̅
𝐿𝑀
5-1: Midsegments
12. Using the picture to the right, list the parallel segments
13. Using the picture to the right, and RT = 15, DT = 10, and DE = 50
a. FE =
b. TF =
14. Find the value of x.
5-2: Perpendicular and Angle Bisectors
15. Find the value of x:
5-3: Bisectors on Triangles and 5-4: Medians and Altitudes
16. Name the point of concurrency for:
c. Medians
d. Angle bisectors
e. Perpendicular bisectors
f. Altitudes
17. Find the value of x:
18. Given that Y is the centroid and WY = 4, find TY and TW.
5-5 Indirect Proof
19. Write the first step in an indirect proof proving that at least one angle is acute.
5-6/5-7: Inequalities within triangles:
20. Can 2, 4, and 6 be the sides of a triangle?
21. List the angles in order from smallest to largest in
22. If two sides of a triangle are 5 and 6, find the range for the third side.
23. Using inequalities compare the two side lengths given:
6-1: Polygon angle sum
24. Find each of the following for a heptagon:
a. Sum of the interior angles
b. Sum of the exterior angles
c. One exterior angle (for a regular heptagon)
d. One interior angle (for a regular heptagon)
6-2: Parallelograms
25. Find the value of the variable given:
e. QT = 3x -5 and TS = 2x + 6
f. 𝑚∠𝑄𝑃𝑆 = 5𝑥 − 1 𝑎𝑛𝑑 𝑚∠𝑄𝑅𝑆 = 3𝑥
g. PQ = 4x – 5 and RS = 7x – 8
h. 𝑚∠𝑄𝑃𝑆 = 6𝑥 − 3 𝑎𝑛𝑑 𝑚∠𝑅𝑄𝑃 = 4𝑥 − 7
6-3: Proving Quadrilaterals are Parallelograms
26. Complete the proof:
6-4: Properties of Rectangles, Rhombuses and Squares
27. Find the measure of each numbered angle in the Rhombus:
28. LMNP is a rectangle. Find the value of x and the length of each diagonal. LN = 9x – 14
and MP = 7x + 4.
29. Find the value of x and y.
6-5: Conditions for Rectangles, Rhombuses, and Squares
30. Can you conclude that each parallelogram is a rectangle, rhombus, or square? Explain.
i. .
b.
c.
31. A carpenter is building a bookcase. How can the carpenter use a tape measure to check
that the bookshelf is rectangular? Justify your answer.
6-6: Trapezoids and Kites
32. Find the measure of each numbered angle:
j. .
b.
33. Find the value of x.
k.
b.
.
7-2: Similar Polygons and 7-3: Proving Triangles are Similar
34. Are the polygons similar? If so, write a similarity statement and find the similarity
statement.
a.
b.
35. The polygons are similar. Find the value of x and y.
b.
b.
7-4: Similarity in Right Triangles
36. Write the similarity statement for the three triangles:
37. What is the geometric mean between 4 and 10?
38. Find the value of each variable:
7-5: Proportions in Triangles
39. Find the value of x: