Topic 4 Review Geometry

If CDEF ≅ KLMN, which of the following is not true?

• DE ≅ LM

• CF ≅ KN

• CD ≅ MN

• ∠C ≅ ∠K

If ∆UVW ≅ ∆EFC, what is the measure of ∠FEC?

• 39

• 47

• 51

• 82

Wanda claims that congruent triangles have equal perimeters. Is she correct? Explain.

• No; although congruent triangles have three pairs of corresponding angles, the corresponding sides may have different lengths.

• No; although congruent triangles have three pairs of corresponding sides, the corresponding angles may have different measures.

• Yes; congruent triangles have equal perimeters even though corresponding sides may have different lengths.

• Yes; each side of a triangle has the same length as its corresponding side in a congruent triangle.

Is ∆XYZ ≅ ∆RST? Explain.

• No; ∆XYZ ≅ ∆TSR.

• No; the triangles don't have thee pairs of congruent angles.

• Yes; the triangles have three pairs of congruent sides and three pairs of congruent angles.

• Yes; the triangles have three pairs of congruent sides.

Could either SSS, SAS, both, or neither be used to prove the triangles on the right are congruent? Explain.

• Both SAS and SSS; all three sides are congruent, and there is a pair of congruent angles between congruent sides.

• SSS; all sides are congruent, but no congruent angles are marked.

• SAS; there is a pair of congruent angles, but no congruent sides are marked.

• Neither; no pairs of congruent sides or congruent angles are marked.

Is there enough information to prove the triangles congruent? If so, would you use SSS or SAS to prove the triangles congruent?

• There is not enough information to prove the triangles congruent.

• The triangles can be proven congruent using SSS.

• The triangles can be proven congruent using SAS.

Maria makes triangular earrings out of wire. If she uses the same amount of wire on each triangle, must all the earrings be congruent? Support your answer.

• Yes; they will be congruent by SSS.

• Yes; they will be congruent by SAS.

• No; the corresponding side lengths will be the same, but the corresponding angle measures could be different.

• No; the perimeters of the earrings are equal, but the corresponding side lengths could be different.

Andy claims that if you know that two sides and an angle of a triangle are congruent to two sides and an angle of a second triangle, then the two triangles are congruent by SAS. Is he correct? Explain.

• Yes; he is correct by the SAS Postulate.

• No; the two triangles are congruent by SSS.

• No; the angle must be between the two sides in each triangle.

• No; more information about the triangles is needed to prove congruence.

If AC bisects ∠BAD, is △ABC ≅ △ADC? Explain.

• Yes; then ∠BAC is congruent to ∠DAC, and the triangles are congruent by ASA.

• then ∠BAC is congruent to ∠CAD, and the triangles are congruent by AAS.

• No; in that case, only two pairs of corresponding congruent angles would be known.

• No; in that case, only one pair of corresponding congruent angles and one pair of corresponding congruent sides would be known.

Can two triangles be non congruent but have one pair of congruent sides and two pairs of congruent angles? Explain.

• No; the triangles would be congruent by ASA.

• No; the triangles would be congruent by both ASA and AAS.

• Yes, if the congruent side between the two angles in one triangle is adjacent to only one of the angles in the other triangle.

• Yes, if the congruent side between the two angles in one triangle is also between the two angles in the other triangle.