Practice Informal Transformational Proof in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An informal transformational proof uses translations, rotations, reflections, and dilations to explain why two figures are congruent or similar.
Instead of measuring sides and angles, show that one shape can be moved, flipped, or resized to land exactly on another.
Showing a random 20 of 50 problems.
Example 1
mediumWhat does it mean if NO sequence of rigid motions maps figure A onto figure B?
Example 2
mediumProve informally that the base angles of an isosceles triangle are congruent using a reflection.
Example 3
mediumProve informally that opposite sides of a parallelogram are congruent using a 180ยฐ rotation about its center.
Example 4
easyWhy is a transformational proof considered valid (not just visual)?
Example 5
mediumAn equilateral triangle has rotational symmetry of what order about its centroid?
Example 6
mediumTriangle A has vertices ; triangle B has . Describe a single transformation mapping A to B.
Example 7
mediumIf you dilate a triangle by a factor of about a vertex, what is the ratio of perimeters of new to original?
Example 8
easyTwo triangles are mirror images of each other and have the same side lengths. What transformation maps one to the other?
Example 9
mediumProve informally that the diagonals of a rectangle are congruent using a reflection.
Example 10
easyWhich property is NOT preserved by a reflection?
Example 11
mediumTwo squares have side lengths 2 and 5. Are they similar? Justify by giving a dilation.
Example 12
hardTwo parallel lines are cut by a transversal. Use a translation along the transversal to argue corresponding angles are congruent.
Example 13
challengeProve informally that a line through the midpoints of two sides of a triangle is parallel to the third side, using a dilation.
Example 14
mediumTriangle A is at ; triangle B is at . What transformation maps A to B?
Example 15
easyWhich transformation preserves both size AND orientation: rotation, reflection, or dilation by 1?
Example 16
mediumWhich sequence guarantees similarity but NOT congruence?
Example 17
easyWhich is NOT preserved under dilation by scale factor ?
Example 18
mediumProve informally that vertical angles are congruent using a 180ยฐ rotation.
Example 19
mediumTwo figures have the same shape but opposite orientation (mirror images) and the same size. What maps one to the other?
Example 20
mediumA square is mapped onto itself by a 90ยฐ rotation about its center. What does this prove about the square?