Question

determine if the triangles are similar. if so, state the similarity transformations.
1.
2.

Explanation:

Problem 1 (Triangle with HJ and MK)

Step1: Identify Parallel Lines

HJ is parallel to MK (given by arrows).

Step2: Use AA Similarity

∠G is common to both △GHJ and △GMK. ∠GHJ = ∠GMK (corresponding angles, since HJ || MK). By AA (Angle - Angle) similarity criterion, △GHJ ~ △GMK. The similarity transformation is a dilation (and possibly a translation/rotation, but mainly the AA similarity due to parallel lines creating corresponding angles equal).

Step1: Calculate Angles in △XYZ

In △XYZ, ∠Z = 90°, ∠X = 50°, so ∠Y = 180° - 90° - 50° = 40°.

Step2: Calculate Angles in △ABC

In △ABC, ∠B = 90°, ∠C = 40°, so ∠A = 180° - 90° - 40° = 50°.

Step3: Apply AA Similarity

∠Z = ∠B = 90°, ∠Y = ∠C = 40° (or ∠X = ∠A = 50°). By AA similarity, △XYZ ~ △ACB (or △XYZ ~ △ABC with appropriate correspondence). The similarity transformation is AA similarity (matching right angles and the 40° (or 50°) angles).

Answer:

The triangles (△GHJ and △GMK) are similar by AA similarity (due to parallel lines creating equal corresponding angles and a common angle). The similarity transformation involves AA similarity (with HJ || MK leading to corresponding angles equal, plus common angle ∠G).

Problem 2 (Right Triangles XYZ and ABC)