Im Geometry

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.

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.

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.

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.

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.

WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZWX has a measure of 60 degrees. Find the measure of angle ZYW.

Angle ZYW has a measure of ______ degrees.

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

Select all true statements based on the diagram.

• Angle CBE is congruent to angle DEA

• Angle CEB is congruent to angle DEA

• Segment DA is congruent to segment CB

• Segment DC is congruent to segment AB

• Line DC is parallel to line AB

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.