Name:______Date:______
Semester 1 Final Exam Review
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles.
1.A carnival ride is drawn on a coordinate plane so that the first car is located at the point . What are the coordinates of the first car after a rotation of 270° about the origin?
What is the solution of each proportion?
2.
3.Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.
4.Where is the circumcenter of any given triangle?
Use the diagram.
5.Find the translation rule that describes the translation BD.
6.Find the image of C under the translation described by the translation rule .
7.You want to draw an enlargement of a design that is printed on a card that is 6 in. by 7 in. You will be drawing this design on an piece of paper that is in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
____8.Supply the missing reasons to complete the proof.
Given: and
Prove:
A. / ASA; Corresp. parts of / C. / SAS; Corresp. parts ofB. / ASA; Substitution / D. / AAS; Corresp. parts of
9.What are the missing reasons in the two-column proof?
Given:
Prove:
Statements / Reasons1. / 1. Given
2. / 2. ?
3. / 3. Given
4. / 4. ?
10.Which lines are parallel if ? Justify your answer.
What are the values of a andb?
11.
12.Use a translation rule to describe the translation of that is 4 units to the right and 8 units down.
Find the geometric mean of the pair of numbers.
13.6 and 7
14.The glide reflection maps the point P to (–7, 3). Find the coordinates of P.
15.Find the values of x and y.
16.The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two angles?
17.List the sides in order from shortest to longest. The diagram is not to scale.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
18.
____19.Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. / I only / B. / III only / C. / I or III only / D. / I, II, or II____20.Which three lengths CANNOT be the lengths of the sides of a triangle?
A. / 18 m, 5 m, 10 m / C. / 23 m, 16 m, 12 mB. / 7 m, 9 m, 8 m / D. / 15 m, 15 m, 11 m
21.Which two triangles are congruent by ASA?
22.Red and grey bricks were used to build a decorative wall. The was . There were 175 bricks used in all. How many red bricks were used?
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
23.In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.
24.A salsa recipe uses green pepper, onion, and tomato in the extended ratio 2 : 3 : 7. How many cups of onion are needed to make 72 cups of salsa?
____25.Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 154 ft from camera 2, which was 100 ft from camera 3. Cameras 1 and 3 were 133 ft apart. Which camera had to cover the greatest angle?
A. / camera 3 / B. / camera 1 / C. / camera 2 / D. / cannot tell26.Supply the reasons missing from the proof shown below.
Given:,
Prove:
27.The vertices of a triangle are P(–4, 1), Q(–4, 4), and R(6, 1). Name the vertices of .
28.The dashed-lined figure is a dilation image of with center of dilation P (not shown). Is an enlargement, or a reduction? What is the scale factor n of the dilation?
29.The legs of an isosceles triangle have lengths and . The base has length . What is the length of the base?
30.The vertices of a triangle are P(5, 6), Q(–2, –2), and R(–8, –3). Name the vertices of .
31.For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes
32.Given and , find and
33.From the information in the diagram, can you prove ? Explain.
What similarity statement can you write relating the three triangles in the diagram?
34.
35.What is the value of x?
36.What is the value of x?
37. bisects Find the value of x. The diagram is not to scale.
____38.If , then = ____.
A. / / B. / / C. / / D. /39.Find the image of P(–1, 2) after two reflections; first , and then .
40.Justify the last two steps of the proof.
Given: and
Prove:
Proof:
1. / 1. Given2. / 2. Given
3. / 3.
4. / 4.
41.The dashed-lined figure is a dilation image of EFGH. Is an enlargement or a reduction? What is the scale factor n of the dilation?
42.Find the value of x. The diagram is not to scale.
43.Name a median for
44.Find the length of the midsegment. The diagram is not to scale.
____45.Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. / I only / B. / II only / C. / I or II only / D. / I, II, or II____46.Two sides of a triangle have lengths 7 and 15. Which inequalities represent the possible lengths for the third side, x?
A. / / C. /B. / / D. /
47.Points B, D, and F are midpoints of the sides of EC = 38 and DF = 23. Find AC.
The diagram is not to scale.
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
48.
____49.If and, which additional statement does NOT allow you to conclude that ?
A. / / C. /B. / / D. /
Semester 1 Final Exam Review
Answer Section
1.
2.–3
3.20 ft
4.the point of concurrency of the perpendicular bisectors of the sides of the triangle
5.
6.(4, 10)
7. in.
8.A
9.2. Reflexive Property
4. Hinge Theorem
10., by the Converse of the Alternate Interior Angles Theorem
11.
12.
13.
14.(–4, 12)
15.
16.15° and 75°
17.
18.x = 9
19.A
20.A
21.
22.125
23.The triangles are not similar.
24.18
25.A
26.SAS; Corresp. parts of
27.
28.reduction;
n =
29.5
30.
31.circumcenter
incenter
centroid
orthocenter
32.7
33.yes, by ASA
34.
35.48°
36.5
37.20
38.C
39.(–5, –12)
40.Reflexive Property of ; SSS
41.n = 3; enlargement
42.
43.
44.46
45.B
46.D
47.46
48.; SAS
49.B