Quiz about IM Geometry Unit 2

Question 1

When rectangle ABCD is reflected across line EF, the image is DCBA. How do you know that segment AB is congruent to segment DC?

Accepted Answer

Corresponding parts of congruent figures are congruent.

Answer

A rectangle has 2 pairs of parallel sides.

Answer

Any 2 sides of a rectangle are congruent.

Answer

Congruent parts of congruent figures are corresponding.

Question 2

Triangle HEF is the image of triangle FGH after a 180 degree rotation about point K. Select all statements that must be true.

Accepted Answer

Angle EHF is congruent to angle FGH

Accepted Answer

EFGH is a rhombus.

Accepted Answer

Diagonal FH bisects angles EFG and EHG

Answer

Angle FEH is congruent to angle FGH

Answer

Diagonal FH is perpendicular to side FE

Question 3

Triangle ABC is congruent to triangle EDF. So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF.

Select all true statements after the transformations:

Accepted Answer

Angle B coincides with angle D.

Accepted Answer

Segment AC coincides with segment EF.

Accepted Answer

Segment AB coincides with segment ED.

Answer

Angle A coincides with angle F

Answer

Segment BC coincides with segment ED.

Question 4

The triangles are congruent. Which sequence of rigid motions will take triangle XYZ onto triangle BCA?

Accepted Answer

Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with B. Reflect X"Y"Z" across line CB

Answer

Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with B. Reflect X"Y"Z" across line AC.

Answer

Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with A. Reflect X"Y"Z" across line CB.

Answer

Translate XYA using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with A. Reflect X"Y"Z across line AC.

Question 5

Triangle ABC is congruent to triangle DEF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

Accepted Answer

Segment BC is congruent to segment EF

Accepted Answer

Angle BAC is congruent to angle EDF

Accepted Answer

Angle CBA is congruent to angle DEF

Answer

Segment AC is congruent to segment EF

Answer

Angle BCA is congruent to angle EDF

Question 6

When triangle ABC is reflect across line AB, the image is triangle ABD. Why is angle ACD congruent to angle ADB?

Accepted Answer

Corresponding parts of congruent figures are congruent.

Answer

Congruent parts of congruent figures are corresponding.

Answer

Segment AB is perpendicular bisector of segment DC

Answer

An isosceles triangle has a pair of congruent angles

Question 7

When rectangle ABCD is reflected across line EF, the image is BADC.

How do you know that segment AD is congruent to segment BC?

Accepted Answer

Corresponding parts of congruent figures are congruent.

Answer

A rectangle has pairs of parallel sides.

Answer

Any 2 sides of a rectangle are congruent.

Answer

Congruent parts of congruent figures are corresponding.

Question 8

Write a sequence of rigid motions to take figure ABC to figure DEF.

Accepted Answer

Translate figure ABC by the directed line segment from C to F . Rotate the image of figure ABC using F as the center so that the image of B coincides with E.

Answer

Rotate figure ABC using B as the center. Translate figure ABC by the directed line segment from C to F so that the image of C coincides with F.

Answer

Translate figure ABC by the directed line segment from C to F. Reflect figure ABC over line segment FE so that the image of A coincides with D.

Answer

Reflect figure ABC over line segment FE so that the image of A coincides with D. Rotate figure ABC using B as the center.

Question 9

Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle DBC is isosceles? Select all that apply.

Accepted Answer

Line AB is an angle bisector of DAC

Accepted Answer

Angle BDC is congruent to angle BCD.

Accepted Answer

Triangle DAB is congruent to triangle CAB

Answer

Angle BAD is congruent to angle ABC.

Answer

Angle ABD is congruent to angle ABC.

Question 10

What triangle congruence theorem could you use to prove triangle ADE is congruent to triangle CDE?

Accepted Answer

Angle-Side-Angle Triangle Congruence

Answer

Side-Angle-Side Triangle Congruence

Answer

Side-Side-SIde Triangle Congruence

Answer

Side-Side-Angle Triangle Congruences

Question 11

Each statement is always true. Select all statements for which the converse is also always true.

Accepted Answer

Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles.

Converse: If 2 lines intersect to form 4 right angles, then they are perpendicular.

Accepted Answer

Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment.

Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.

Accepted Answer

Statement: In an isosceles triangle, the base angles are congruent.

Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.

Answer

Statement: If 2 angles are vertical, then they are congruent.

Converse: If 2 angles are congruent, then they are vertical.

Answer

Statement: If 2 angles form a straight angle, then they are supplementary.

Converse: If 2 angles are supplementary, then they form a straight angle.

Question 12

In isosceles triangle DAC, AD is congruent to AC. Karl knows that the base angles of an isosceles triangle are congruent. Select all the choices that would allow Karl to show that AB is a perpendicular bisector of segment CD.

Accepted Answer

AB is an angle bisector.

Accepted Answer

DB is congruent to BC.

Accepted Answer

AB is perpendicular to DC.

Accepted Answer

Angle ABD is congruent to angle ABC.

Answer

AB is congruent to itself.

Question 13

Triangle DAC is isosceles.

What information do you need to show that triangle DBA is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence Theorem?

Accepted Answer

Angle BAD is congruent to angle BAC.

Answer

DC is congruent to itself.

Answer

Angle ABD is congruent to angle BAC.

Answer

Angle BAD is congruent to angle BCA.

Question 14

Refer to the figures.

Which of the following is a sequence of rigid motions to take figure CBA to figure MLK?

Accepted Answer

Translate figure ABC by the directed line segment from C to M. Rotate the image of figure ABC using M as the center so that the image of B coincides with L.

Answer

Translate figure ABC by the directed line segment from B to L. Rotate the image of figure ABC using M as the center so that the image of A coincides with M.

Answer

Reflect figure ABC across segment CL. Reflect the image of figure ABC across segment BL.

Answer

There isn't a sequence of rigid motions to take figure CBA to figure MLK.

Question 15

Select all true statements based on the diagram.

Accepted Answer

Angle CEB is congruent to angle DEA

Accepted Answer

Segment DA is congruent to segment CB

Answer

Angle CBE is congruent to angle ABE

Answer

Segment DC is congruent to segment AB

Question 16

Select all true statements based on the diagram.

Accepted Answer

Angle CEB is congruent to angle DEA

Accepted Answer

Segment DA is congruent to segment CB

Accepted Answer

Line DC is parallel to line AB

Answer

Angle CBE is congruent to angle DEA

Answer

Segment DC is congruent to segment AB

Question 17

The triangles are congruent. Which sequence of rigid motions takes triangle DEF onto triangle DEF onto triangle BAC.

Accepted Answer

Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with B. Reflect D"E"F across line AB.

Answer

Translate DEF using directed line segment. EA. Rotate D'E'F' using A as the center so that D' coincides with C. Reflect D"E"F" across line AC

Answer

Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with C. Reflect D"E"F" across line AB.

Answer

Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with B. Reflect D"E"F across line AC.

Question 18

Lin is using the diagram to prove the statement, "If a parallelogram has one right angle, it is a rectangle." Given that EFGH is a parallelogram and angle HEF is right, which reasoning about angles will help her prove that angle FGH is also a right angle?

Accepted Answer

Opposite angles in a parallelogram are congruent.

Answer

Corresponding angles are congruent when parallel lines are cut by a transversal.

Answer

Vertical angles are congruent.

Answer

The base angles of an isosceles triangles are congruent.

Question 19

What conjecture is possible to prove?

Accepted Answer

If the three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent.

Answer

If the four angles in a quadrilateral are congruent to the four angles in another quadrilateral, then the two quadrilaterals are congruent.

Answer

If the four sides in a quadrilateral are congruent to the four sides in another quadrilateral, then the two quadrilaterals are congruent.

Answer

If the three angles in a triangle are congruent to the three angles in another triangle, then the two triangles are congruent.

Question 20

Select the statement that must be true.

Accepted Answer

If a quadrilateral has opposite sides that are both congruent and parallel, then it is a parallelogram.

Answer

Parallelograms have at least one right angle.

Answer

Parallelograms have congruent diagonals.

Answer

The height of a parallelogram is greater than the lengths of the sides.

Question 21

EFGH is a parallelogram and angle HEF is a right angle.

Select all statements that must be true.

Accepted Answer

EFGH is a rectangle

Accepted Answer

Triangle HEF is congruent to triangle FGH

Accepted Answer

ED is congruent to HD, DG, and DG

Answer

Triangle HEF is congruent to triangle GFH

Answer

Triangle EDH is congruent to triangle HDG

IM Geometry Unit 2

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