Geometry

Q: Given: FH ⊥ GH; KJ ⊥ GJ Prove: ΔFHG ~ ΔKJG Identify the steps that complete the proof.

A: ♣ = all right angles are congruent ♦ = angle FHG is congruent to angle KGJ ♠ = AA similarity theorem

Q: Given: XY || ZW Prove: △XYV ~ △ZWV

A: * If XZ is a transversal that intercepts XY and ZW, angle YXV and angle WZV are alternate interior angles. * Since XY is parallel to ZW, we know that these angles are congruent. * We also know that angle XVY and angle ZVW are vertical angles, and thus congruent. * We can conclude that △XYV ~ △ZWV using the AA similarity theorem.

Q: Determine the similarity transformations that verify △ABC ~ △A''B''C'.

A: * The first transformation mapping △ABC to △A'B'C' is a translation left. * The second transformation mapping △A'B'C' to △A''B''C' is a dilation with center C'

Q: What additional information could be used to prove that △ABC ~ △NML? Check all that apply.

A: * ∠B ≅ ∠M * △ABC was rotated and dilated by a scale factor between 0 and 1. * ∠C ≅ ∠L

Q: The composition DO,0.75(x,y) ∘ DO,2(x,y) is applied to △LMN to create △L''M''N''. Which statements must be true regarding the two triangles? Check all that apply.

A: * ∠M ≅ ∠M'' * LMN ~ △L''M''N'' * The coordinates of vertex N'' are (3, -1.5).

Q: Triangle DEF is similar to triangle D'E'F'. Which similarity transformation could map △DEF to △D'E'F'?

A: rotation and dilation

Q: Given: m∠B = 46°; m∠C = 45°; m∠R = 46°;m∠T = 89° Prove: △ABC ~ △TRS Melissa believes that the AA similarity theorem can prove that the triangles are similar. Which fact would be necessary in the proof?

A: The sum of the measures of the interior angles of a triangle is 180°.

Q: Triangle XYZ was reflected across m and then dilated to form a similar triangle. Which triangle represents the image?

A: the 2nd one