Showing Triangles Congruent

If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, the triangles are congruent. Note that ___ ≅ is equivalent to AAS ≅.

• HL

• ASA

• SAS

• SSS

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.

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.

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

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

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

• Side-Angle-Side Triangle Congruence

• Angle-Side-Angle Triangle Congruence

• Side-Side-SIde Triangle Congruence

• Side-Side-Angle Triangle Congruences

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.

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

• 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

• 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.

• 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.

• 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.

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

• Angle FEH is congruent to angle FGH

• EFGH is a rhombus.

• Diagonal FH bisects angles EFG and EHG

• Diagonal FH is perpendicular to side FE

• Angle EHF is congruent to angle FGH

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.