Directed Line Segment Geometry

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

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.

Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU?

• Rotate GHJ using center G until GH is lined up with ST and then reflect over a line halfway between G'H'J' and STU.

• Translate GHJ by the directed line segment GS. Rotate G'H'J' using S as the center by angle H'ST. Reflect G''H''J'' over ST.

• Translate GHJ by the directed line segment GT. Rotate G'H'J' using T as the center by angle H'TS. Reflect G''H''J'' over ST.

• Translate GHJ by the directed line segment GS.Translate G'H'J' by the directed line segment H'T. Translate G''H''J'' by the directed line segment J''T.

Reflect triangle STU across line ST. Which of these is a valid reason why the image of U will coincide with J?

• The image of U and J are on the same side of ST and make the same angle with it at T.

• The image of U and J are the same distance along the same ray from T.

• The image of U and J will not coincide after reflection over ST.

• Line ST is the perpendicular bisector of the segment connecting U and J, because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment.

Here is parallelogram ABCD. Prove segment AM is congruent to segment CM.

Evaluate responses using AI:

OFF

Is triangle EJH congruent to triangle EIH? Explain your reasoning.

Evaluate responses using AI:

OFF

Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1, -3) and B has coordinates (8,9), find the coordinates of M.

• (2, 1)

• (5/3, 0)

• (5, 5)

• (23/3, 8)

Find the coordinates of P so that P partitions segment AB in the ratio 5:1 with A = 2 and B = 8.

• P = 7

• P = 9

• P = -3

• P = 5

Find 1/4 of the way from the left point to the right point.

• (2.5, 2.5)

• ( - 0.5, 1.5)

• ( - 0.5, 2.5)

• (2.5, 1.5)