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Review Day 5 Practice-Triangle Congruence & Parallel Lines.

1.Triangle  is rotated, reflected, and translated to yield triangle . 

 Which statement proves that the two triangles are congruent?A. is taken to , and is taken to .B. is taken to , and is taken to .C. is taken to , is taken to , and is taken to .D. is taken to , is taken to , and is taken to .

 

2.All vertices of an equilateral triangle are shifted 5 units to the left to create a new triangle. Which statement uses the concepts of rigid motion and the congruence theorems for triangles to explain whether the triangles are congruent?

A. The triangles are not congruent because enlarging the triangle by 5 units changes the angles.B. The triangles are congruent because all angles were maintained to form a new equilateral triangle.C. The triangles are congruent because shifting the triangle does not change the side lengths of the triangle.D. The triangles are not congruent because increasing each of the side lengths by the same number of units

creates a similar triangle. 3.

is reflected across the y-axis.  Which set of congruence statements explains why the triangles are congruent?

A. and ; : SASB. and ; : ASAC. ; ; : SSSD. ; ; : AAA

4. Triangle   is rotated to become triangle . Without the use of any measurement devices, which statement could be used to prove that triangle   is congruent to triangle ?

A. ASA because both are right triangles and is congruent to .B. SAS because both are right triangles, is congruent to , and is

congruent to .C. SAS because both are right triangles, is congruent to , and is

congruent to .D. ASA because both are right triangles, is congruent to , and is

congruent to .

5.In the figure below, triangle  is congruent to triangle .    Which transformation would maintain the congruence of the triangles? I. Reflecting triangle  over II. Rotating triangle  clockwise  about point III. Dilating triangle  by , with  as the center of dilation

A. I onlyB. III onlyC. I and II onlyD. II and III only

 6. Triangle   is rotated to become triangle  . 

 Without the use of any measurement devices, which could be used to prove that triangle  is congruent to triangle ?

A. ASA because both are right triangles and is congruent to B. SAS because both are right triangles, is congruent to , and is

congruent to C. SAS because both are right triangles, is congruent to , and is

congruent to D. ASA because both are right triangles, angle is congruent to angle , and

is congruent to

7.Lines and are parallel. The , and the  . 

 Which statement explains why you can use the equation to solve for ?

A. Alternate exterior angles are congruent.B. Alternate interior angles are congruent.C. Complementary angles are congruent.D. Corresponding angles are congruent.

 

8. Janice is constructing a formal proof using this figure. Janice wants to prove that the angle bisector of  is the median of . What must she prove to meet her conclusion?

A. is a right angle.B. is congruent to .C. is an obtuse angle.D. is proportional to .

9.Rosie constructs a triangle between two parallel lines, a and b. 

 If and , what is ?

A.B.C.D.

10. Given:  

 Which statement must be true?

A.B.C.D.

11.In the figure shown below, .

  What is the measure of ?

A.B.C.D.

 

12.

Given: with transversal  

 What is the measure of ?A.B.C.D.

13.A portion of a chainlink fence is shown below. Wires pointing in the same direction are parallel.

 

 What is the measure of  ?

A.B.C.D.

14.Dogwood Lane, Apple Blossom Lane, and Willow Lane are parallel, as shown on the map below. 

 What is the value of ?

A. 70B. 80C. 100D. 110

15.For an art project, Melody folded a piece of paper as shown. 

 What is the value of ?

A. 132B. 66C. 48D. 24

16.In Jane’s diagram,  is the transversal of and . Which statement could Jane use to prove  is parallel to

?

A. Adjacent angles are congruent.B. Corresponding angles are congruent.C. Same-side interior angles are congruent.D. Same-side exterior angles are congruent.

 

17.Olivia drew two parallel lines, and . She then drew a transversal, , through the two parallel lines. She found that four marked angles had the same measure.  

 Which conclusion can Olivia draw about the measures of the remaining four angles?

A. None of the four measures are equal.B. Only two of the four measures are equal.C. All four measures are equal, and the angles are supplementary

to the marked angles.D. All four measures are equal, and the angles are complementary

to the marked angles.

 

18. Richie was given the following statements and corresponding reasons and was asked to put them together in the right order to complete a proof.  

Given: is a rhombus.Prove:   is complementary to . 

 Which is the correct order of these statements and reasons?

A. 3, 4, 1, 6, 2, 5B. 3, 4, 2, 6, 1, 5C. 5, 4, 3, 1, 6, 2D. 3, 1, 4, 2, 5, 6

 19. Look at the figure below. Line   is parallel to line . The transversal line   intersects lines  and . Which statement demonstrates the angles that are congruent to  and why they are congruent to ?

A. (vertical angles); (alternate interior angles); (corresponding angles)

B. (alternate interior angles); (vertical angles); (corresponding angles)

C. (alternate interior angles); (vertical angles); (corresponding angles)

D. (vertical angles); (alternate interior angles); (corresponding angles)

 20.In proving that the interior angles of a Triangle add to 180 degrees, it must be shown that:   

 What is an appropriate rationale for this statement?

A. Additive PropertyB. Angle Sum TheoremC. Linear Pair TheoremD. Angle Bisector Theorem

 

21.In the figure below,  , and .  

 

What is ?

A.B.C.D.

 22.In a flow proof of the Exterior Angle Theorem, what step should come between step 1 and step 3 below? 1.    and   2. ??? 3.  

A.B.C.D.

 23.In the figure to the right, the measure of  is . What is the measure of ?

A.B.C.D.

24.Craig is going to write an indirect proof of the problem below. Given:  Lines l and m are cut by transversal t.            Alternate interior angles are congruent.Prove: Lines l and m are parallel. Which statement must be assumed as the first step of Craig’s proof?

A. Lines l and m are not parallel.B. Lines l and m are not cut by transversal t.C. Alternate interior angles are not congruent.D. Lines l and m are not cut by transversal t, and alternate interior angles are not congruent.

25. In proving the exterior angles of a quadrilateral add to  degrees, it must be shown that: 

  

 What is the appropriate rationale for this statement?

A. Angle Addition TheoremB. Definition of a Linear PairC. Definition of Supplementary AnglesD. Definition of Complementary Angles

 26. The flow proof  below shows the interior angles of a quadrilateral thats adds up to degrees. What is the missing step? Step 1:

 Step 2:  ? Step 3:

 Step 4:

A.B.C.D.

 

27.On the right is triangle ABC and a line parallel to BC through point A. 

 In the proof below, which reason justifies statement 7? 

A. Consecutive Angles TheoremB. Corresponding Angles TheoremC. Alternate Interior Angles TheoremD. Alternate Exterior Angles Theorem

 28.Consider the figure shown, in which .  

  Which step or fact is not necessary to prove that ?

A. is a right angle.B. Vertical angles are congruent.C. is the midpoint of segment .D. In a plane, only one line perpendicular to a given line can be drawn through a

point that doesn’t belong to the line.

 29.Let  be the perpendicular bisector to segment , and let . Which step or principle is not necessary in the proof of the theorem: “A point in the perpendicular bisector  of segment  is equidistant from the segment’s endpoints”?

A. definition of the midpoint of a segmentB. SAS: If two sides in one triangle are congruent to two sides of a second triangle, and also the included angles

are congruent, then the triangles are congruent.C. ASA: If two angles in one triangle are congruent to two angles of a second triangle, and also the included sides

are congruent, then the triangles are congruent.D. CPCTC: Congruent parts of congruent triangles are congruent. 

30.In the figure below, points  , , and  are collinear and  is a right angle. Lydia uses the proof below to show that  and  are complementary angles.    Which is a correct reason for step  of the proof?

A. definition of complementary anglesB. definition of supplementary anglesC. definition of angle bisectorD. definition of right angle

 

 32.As part of a proof, Jessica drew two intersecting lines and labeled the resulting angles 1, 2, 3, and 4. 

 Which reason completes Jessica’s proof?

A. GivenB. Adjacent angles are supplementary.C. Corresponding parts of congruent triangles are congruent.D. If angles are supplementary to the same angle, they are

congruent. 

31.In the figure below,  and line  is transversal. 

 Which of these is an accurate proof of the Alternate Interior Angles Theorem?

A.

B.

C.

D.