IM Geometry Midterm Exam Ch 1-2

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:

• Angle A coincides with angle F

• Angle B coincides with angle D.

• Segment AC coincides with segment EF.

• Segment BC coincides with segment ED.

• Segment AB coincides with segment ED.

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

• Corresponding parts of congruent figures are congruent.

• Congruent parts of congruent figures are corresponding.

• Segment AB is perpendicular bisector of segment DC

• An isosceles triangle has a pair of congruent angles

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

• 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.

• 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.

• 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.

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

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

• 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

• 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.

• 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.

• 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.

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

• A rectangle has 2 pairs of parallel sides.

• Any 2 sides of a rectangle are congruent.

• Congruent parts of congruent figures are corresponding.

• Corresponding parts of congruent figures are congruent.

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.

• AB is an angle bisector.

• DB is congruent to BC.

• AB is congruent to itself.

• AB is perpendicular to DC.

• Angle ABD is congruent to angle ABC.

Select all true statements based on the diagram.

• Angle CBE is congruent to angle ABE

• Angle CEB is congruent to angle DEA

• Segment DA is congruent to segment CB

• Segment DC is congruent to segment AB

Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.

Which of the following equations must be true based on the figure?

• 60+58+x=180

• 60+y=x

• 60+58=x

• 58+y=x

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

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

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

• 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.

• 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.

• 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.

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

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