Geometry

Triangle ABC is rotated 45° about point X, resulting in triangle EFD. Triangle A B C is rotated 45 degrees about point X to form triangle E F D. The lengths of sides A C and D E are congruent, the lengths of sides A B and E F are congruent, and the lengths of sides D F and C B are congruent. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB?

3.6 cm

Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto's proof that was not included in Nessa's proof? Given: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right Prove: TriangleABC ≅ TriangleQNM

Angle<A ≅ Angle<Q because of the third angle theorem.

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

AngleFGH ≅ AngleKGJ because vertical angles are congruent.

Which congruence theorem can be used to prove △BDA ≅ △DBC? Triangles B D A and D B C share side D B. Angles C B D and A D B are right angles. Sides C D and B A are congruent.

HL

Which best explains whether or not ΔABC ≅ ΔLMN?

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

Which best explains whether or not triangles RST and ACB are congruent?

The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.

What are the rigid transformations that will map △ABC to △DEF?

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.

Could ΔABC be congruent to ΔADC by SSS? Explain.

Yes, but only if BC ≅ DC.

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters. Is ΔWXZ ≅ ΔYZX? Why or why not?

Yes, they are congruent by SAS.

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F. Which rigid transformation would map ΔABC to ΔABF?

a reflection across the line containing BA

Which rigid transformation would map TriangleABC to TriangleEDC?

a rotation about point C

Triangle DEF is congruent to TriangleD'EF' by the SSS theorem. Which single rigid transformation is required to map TriangleDEF onto TriangleD'EF'?

rotation

How can ΔABC be mapped to ΔXYZ? Triangles A B C and X Y Z are shown. The lengths of sides A B and X Y are 25 centimeters. The lengths of sides A C and X Z are 29 centimeters. Angles B A C and Y X Z are 36 degrees. Triangle A B C is slightly higher and to the left of triangle X Y Z. Triangle A B C is rotated to form triangle X Y Z. First, translate ____________________. Next, rotate ΔABC about B to align the sides and angles.

vertex B to vertex Y

Triangle RST is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures?

ΔRST ≅ ΔBAC