Geometry Triangles Center

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.

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

• Segment AC is congruent to segment EF

• Segment BC is congruent to segment EF

• Angle BAC is congruent to angle EDF

• Angle BCA is congruent to angle EDF

• Angle CBA is congruent to angle DEF

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.

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.

• Line AB is an angle bisector of DAC

• Angle BAD is congruent to angle ABC.

• Angle BDC is congruent to angle BCD.

• Angle ABD is congruent to angle ABC.

• Triangle DAB is congruent to triangle CAB

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.

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.

What conjecture is possible to prove?

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

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

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

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

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?

• DC is congruent to itself.

• Angle ABD is congruent to angle BAC.

• Angle BAD is congruent to angle BCA.

• Angle BAD is congruent to angle BAC.

Triangle ABC can be taken to Triangle A'B'C' using rigid motions and a dilation. Select the true equation:

Triangle ABC is similar to Triangle EFD. What scale factor is required to dilate triangle ABC so that its image, A'B'C' is congruent to triangle EFD?

• 2/5

• 1/2

• 2

• 3