• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript
```Geometry
Winter Review
2014-2015
Name: __________________________________________________ Date:_______________________
MAFS.912.G-CO.4.12
1. Below is a stage in the construction of a line segment congruent to AB with point C as one of the endpoints
of the new line segment.
A.
B.
C.
D.
Which of the following sentences describes the next step in the construction?
Set the compass point on point B and adjust the compass width to point C.
Mark a point on ̅̅̅̅
and adjust the compass width to point C from the point.
̅̅̅̅ and make two arcs on
̅̅̅̅ centered at the point.
Mark a point on
Set the compass point on point A and adjust the compass width to point B.
A.
B.
C.
D.
MAFS.912.G-CO.1.2
2. Which of the following transformations does not preserve distance and angle measures?
translation
reflection
rotation
horizontal stretch
MAFS.912.G-CO.2.6
3. Is triangle  congruent to triangle ?
A. Yes. Triangle STU was rotated clockwise 270° about point T, translated 7 units to the right, and translated 6 units
down to create triangle WXY.
B. Yes. Triangle STU was rotated clockwise 270° about point T, translated 4 units to the right, and translated 2 units
down to create triangle WXY.
C. No. Triangle STU is not congruent to triangle WXY.
D. Yes. Triangle STU was rotated clockwise 90° about point T, translated 7 units to the right, and translated 6 units
down to create triangle WXY.
Geometry
Winter Review
2014-2015
MAFS.912.G-CO.4.12
4. Amy made a mistake in creating a copy of ∠. What does she need to correct in the following
construction for copying ∠ with point  as the vertex of the new angle?
A.
B.
C.
D.
The second arc should be centered at point J and pass through point A.
The third arc should be centered at point K and pass through point E.
The second arc should be centered at point H and pass through point A.
The third arc should be centered at point K and intersect the second arc.
MAFS.912.G-CO.1.3
5. If ∠ ≅ ∠, which of the following conditions must also be met to prove that ∆ ≅ ∆ by AngleAngle-Side rule?
A.
B.
C.
D.
I only
I or IV only
II only
III or IV only
Geometry
Winter Review
MAFS.912.G-CO.1.3
6. Which transformation carries the regular hexagon EFGHIJ onto itself?
A.
B.
C.
D.
a rotation of 60° about its center
a rotation of 45° about its center
a rotation of 90° about its center
a rotation of 30° about its center
MAFS.912.G-CO.3.10
7. Given: ∆ with exterior ∠4
Prove: ∠4 = ∠1 + ∠2
Proof:
Which of the following reasons completes the proof?
A.
B.
C.
D.
∠4 + ∠3 = ∠1 + ∠2 + ∠4
∠1 + ∠3 + ∠4 = 180°
∠1 + ∠2 + ∠4 = 180°
∠4 + ∠3 = ∠1 + ∠2 + ∠3
2014-2015
Geometry
Winter Review
2014-2015
MAFS.912.G-CO.2.7
8. Triangles ABC and DEF have two sets of sides of the same length and the included angles between those
sides have the same measure as shown below.
Which of the following point transformations is a result of a sequence of rigid motions that can be used to
show that triangle ABC is congruent to triangle DEF by taking triangle ABC onto triangle DEF?
A.
B.
C.
D.
(, )  (− + 7, −)
(, )  (−, − + 7)
(, )  (−, − + 7)
(, )  (− + 7, −)
MAFS.912.G-CO.4.12
9. What is the first step in the construction of an angle bisector using only a compass and straightedge?
A. Mark a point in the angle's interior and draw an arc centered at the point, intersecting both the legs of the
angle.
B. Place the compass needle on one of the legs of the angle and draw an arc intersecting the other leg.
C. Mark a point outside the angle and draw an arc centered at the point, intersecting the vertex of the angle.
D. Place the compass needle on the vertex of the angle and draw an arc across both legs of the angle.
MAFS.912.G-CO.2.7
10. A series of transformations were applied to triangle  to create triangle .
If triangle JKL and triangle XYZ are congruent, which of the following transformations could have been
applied to triangle JKL?
A.
B.
C.
D.
I and III only
I, II, III, and IV
I, II, and III only
I and II only
Geometry
Winter Review
MAFS.912.G-CO.3.9
11. Given:  ∥  and u is a transversal of s and t.
Prove: ∠1 ≅ ∠5, ∠2 ≅ ∠6, ∠3 ≅ ∠7,  ∠4 ≅ ∠8
2014-2015
Proof:
Which of the following reasons completes the proof?
A.
B.
C.
D.
Two lines cut by a transversal which has a pair of congruent corresponding angles are parallel.
Two lines cut by a transversal which has a pair of congruent exterior angles are parallel.
Parallel angles postulate.
Converse of the parallel angles postulate.
MAFS.912.G-CO.1.2
12. Which of the following transformations will produce a similar, but not congruent figure?
A.
B.
C.
D.
dilation
reflection
rotation
translation
Geometry
Winter Review
MAFS.912.G-CO.3.9
13. Given: ∠2 and ∠3 are a linear pair,
∠3 and ∠4 are a linear pair
Prove: ∠2 ≅ ∠4
Proof:
Which of the following reasons completes the proof?
A.
B.
C.
D.
Transitive property
Linear pair postulate
Congruent complements theorem
Right angle congruence theorem
MAFS.912.G-CO.1.3
14. Which transformation carries the regular pentagon below onto itself?
A.
B.
C.
D.
a rotation of 36° about the origin
a rotation of 45° about the origin
a rotation of 115° about the origin
a rotation of 72° about the origin
2014-2015
Geometry
Winter Review
MAFS.912.G-CO.2.8
15. Triangle  is rotated clockwise 90° to create triangle .
2014-2015
Is triangle MNO congruent to triangle UVW?
A.
B.
C.
D.
Yes, the triangles are congruent by SSS.
There is not enough information to determine if the triangles are congruent.
No, the triangles are not congruent.
Yes, the triangles are congruent by AAA.
MAFS.912.G-CO.1.5
16. What are the coordinates of ′ if ′′′′ is a reflection of  across the  − ?
A.
B.
C.
D.
(-5,-5)
(-5,-1)
(3,1)
(5,1)
MAFS.912.G-CO.3.10
17. If ∆ is an equilateral triangle and ∠ = 34°, what is ∠?
A.
B.
C.
D.
26°
19°
46°
86°
Geometry
Winter Review
MAFS.912.G-CO.1.5
18. What is the rule for the transformation below?
A.
B.
C.
D.
(′ , ′)
(′ , ′)
(′ , ′)
(′ , ′)
=
=
=
=
2014-2015
(− − 6 , − + 1)
( − 6 , − + 1)
( − 6 ,  − 1)
( − 6 ,  + 1)
MAFS.912.G-CO.1.5
19. Which of the following sequences of transformations will carry rectangle A onto rectangle B?
A.
B.
C.
D.
Rotate rectangle A 90° counterclockwise about the origin, reflect it over the y-axis, and translate it 1 unit up.
Translate rectangle A 7 units down, rotate it 180° about the point (2, -6), and translate it 8 units to the left.
Reflect rectangle A over the x-axis, translate it 2 units up, and reflect it over the y-axis.
Rotate rectangle A 90° clockwise about the origin, and translate it 2 units upand 6 units to the right.
Geometry
Winter Review
MAFS.912.G-CO.2.8
20. Triangle  is translated to create triangle .
2014-2015
Is triangle JKL congruent to triangle RST?
A.
B.
C.
D.
Yes, the triangles are congruent by AAA.
Yes, the triangles are congruent by SAS.
There is not enough information to determine if the triangles are congruent.
No, the triangles are not congruent.
MAFS.912.G-CO.3.9
21. In the picture below, two lines intersect at point F. Angle AFC is represented by (9x)° and angle AFB is
represented by (225 - 14x)°.
Picture not drawn to scale
What is the measure of BFD?
A.
B.
C.
D.
91°
90°
9°
81°
MAFS.912.G-CO.3.9
22. Lines f and g are parallel lines cut by the transversal d. If the measure of ∠2 is 51°, what is the measure of ∠8?
A.
B.
C.
D.
Picture not drawn to scale
129°
61°
51°
119°
Geometry
Winter Review
MAFS.912.G-CO.1.1
23. Which of the following statements is the definition of parallel lines?
A.
B.
C.
D.
2014-2015
Two distinct coplanar lines that intersect at a 90°angle.
Two distinct coplanar lines that do not intersect.
Two rays with a common endpoint that point in opposite directions.
Two rays sharing a common endpoint.
MAFS.912.G-GPE.2.6
24. In the reflection of a polygon, which of the following characteristics of the polygon remain the same?
A.
B.
C.
D.
I and III
I and II
I, II, III
II and III
MAFS.912.G-GPE.2.7
25. A triangle is shown on the coordinate plane below.
What is the perimeter of the triangle?
A.
B.
C.
D.
10.63 units
25.63 units
28 units
56 units
Geometry
Winter Review
2014-2015
MAFS.912.G-SRT.1.1
26. Which of the following represents a polygon that is two times the size of the original polygon?
A.
B.
C.
D.
MAFS.912.G-CO.3.10
27. Given isosceles trapezoid ABCD with ̅̅̅̅
≅ ̅̅̅̅
and ∠ ≅ ∠, determine the missing reason to
prove ∆ ≅ ∆.
A.
B.
C.
D.
alternate exterior angles conjecture
alternate interior angles conjecture
vertical angle conjecture
corresponding angles conjecture
Geometry
Winter Review
2014-2015
MAFS.912.G-CO.3.10
̅̅̅̅ and point E is the midpoint of segment
̅̅̅̅ .
28. Given: Point D is the midpoint of
̅̅̅̅
̅̅̅̅ ∥
Prove:
Proof:
Which of the following reasons complete the proof?
A.
B.
C.
D.
Angle-Angle similarity postulate
Triangle Midsegment Theorem
Side-Angle-Side similarity theorem
Side-Side-Side similarity theorem
MAFS.912.G-SRT.1.1
29. If the scale factor of a dilation is less than one and greater than zero, what happens to the resulting image?
A.
B.
C.
D.
The resulting image will be a rotation of the original image.
The resulting image will be an enlargement of the original image.
The resulting image will be a reduction of the original image.
The resulting image will be a translation of the original image.
Geometry
Winter Review
MAFS.912.G-CO.3.10
30. Complete this proof of the isosceles triangle theorem.
Given: ∆ is isosceles
Construct: ray BD bisecting ∠
Prove: ∠ ≅ ∠
A.
B.
C.
D.
SSS congruence
SAS congruence
AAS congruence
SSA congruence
2014-2015
```
Document related concepts

Line (geometry) wikipedia, lookup

Euclidean geometry wikipedia, lookup

Pythagorean theorem wikipedia, lookup

History of geometry wikipedia, lookup

Rational trigonometry wikipedia, lookup

Integer triangle wikipedia, lookup

Geometrization conjecture wikipedia, lookup

Trigonometric functions wikipedia, lookup

History of trigonometry wikipedia, lookup

Euler angles wikipedia, lookup

Reuleaux triangle wikipedia, lookup

Rotation matrix wikipedia, lookup

Rotation formalisms in three dimensions wikipedia, lookup

Plane of rotation wikipedia, lookup

Similar