Geometry Unit 4

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

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.

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.

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

• 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.

• 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.

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

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

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.

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?

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

• Opposite angles in a parallelogram are congruent.

• Vertical angles are congruent.

• The base angles of an isosceles triangles are congruent.

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

Select all statements that must be true.

• EFGH is a rectangle

• Triangle HEF is congruent to triangle GFH

• Triangle HEF is congruent to triangle FGH

• ED is congruent to HD, DG, and DG

• Triangle EDH is congruent to triangle HDG

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

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