Congruence

Manuela claims that 

 $\overline{AB}\ \ and\ \ \ \overline{PQ}$  
are congruent.

Which statement best describes her claim?

• She is incorrect because the segments do not have the same orientation.

• She is incorrect because the segments do not have the same length.

• She is correct because the segments have the same length.

• She is correct because the segments have the same orientation.

Kris claims that the two figures must be congruent.

Which statement best describes his claim?

• He is correct because both figures are triangles.

• He is correct because the measures of the angles are the same in both figures.

• He is incorrect because the triangles are not oriented the same way.

• He is incorrect because the lengths of the corresponding sides of the figures are unknown.

Linnea has drawn a line from one corner of a rectangle to the opposite corner. The line divides each of the right angles into two angles of measures 32° and 58°. Which statement best describes the resulting triangles?

• The two triangles are not congruent because the corresponding sides do not have the same length.

• The two triangles are congruent but are oriented differently.

• The two triangles may be congruent, but additional information is needed about the angle measures.

• The two triangles may be congruent, but additional information is needed about the side lengths.

Jermaine knows that traingles QRS and FGH each have two sides that are 9 mm long. What statement best describes the two triangles?

• The two triangles are congruent because there are two pairs of congruent corresponding sides.

• The two triangles are congruent because both triangles are isosceles with 9 mm sides.

• The two triangles may be congruent, but additional measurements are needed.

• The two triangles may be congruent, but additional information is needed about the orientation of the figures.

Jermaine knows that traingles QRS and FGH each have two sides that are 9 mm long. What statement best describes the two triangles?

• The two triangles are congruent because there are two pairs of congruent corresponding sides.

• The two triangles are congruent because both triangles are isosceles with 9 mm sides.

• The two triangles may be congruent, but additional measurements are needed.

• The two triangles may be congruent, but additional information is needed about the orientation of the figures.

Joaquin drew the triangle above.

Which statement must be true about a figure that is congruent to Joaquin’s triangle?

• It has two angles on the x-axis.

• It has a side that is 9 units long.

• It has a side that lies on the x-axis.

• It has an obtuse angle.

Amber believes triangle ABC and triangle GFE are congruent. She has recorded the measures of some of the angles and the lengths of some of the sides in the triangles below.

What additional measurement would support Amber’s hypothesis?

• The measure of angle C is 32°.

• The measure of angle C is 40°.

• The measure of angle C is 50°.

• The measure of angle C is 90°.

Deepak is measuring sides and angles of triangle FGH to determine whether it is congruent to triangle MNP shown below.

Deepak found that angle G has a measure of 50° and FH is 18.3 centimeters long. Does he need to continue measuring sides and angles of triangle FGH and why?

• No, he knows that the triangles are congruent because there are corresponding sides and angles that are congruent.

• No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.

• Yes, he must verify that the other two side lengths and the other two angle measures are the same as those found in triangle MNP.

• Yes, he must only verify that the other two angle measures are the same as those found in triangle MNP.

Rectangle JKLM is congruent to a 4 inch by 7 inch rectangle. How many different values are possible for the length of JM?

• 1

• 2

• 3

• 4

Which statement is true?

• A scalene triangle and a right triangle are always congruent.

• A scalene triangle and a right triangle are never congruent.

• An equilateral triangle and a right triangle are always congruent.

• An equilateral triangle and a right triangle are never congruent.