Angles & Lines
Create a rule for spotting angles in objects without measuring them. Explain why your rule works.
Look for two edges or sides that meet at a point. This works because angles are formed by two rays sharing an endpoint.
Explain how you can tell if a transformation changes the size of a figure.
If the shape gets bigger or smaller, it’s not an isometry. If size stays the same, it is.
Explain how you can estimate an angle of rotation without a protractor.
Compare the direction the figure points before and after; estimate the turn needed.
Explain the difference between a segment and a ray using real‑life examples.
A segment has two endpoints; a ray has one endpoint and goes forever in one direction.
Explain what it means for two shapes to be congruent using transformations.
Congruent shapes can be matched exactly using flips, turns, or slides.
Two lines might be parallel. Explain how you can prove corresponding angles are congruent using only reasoning.
If alternate interior angles are equal, then corresponding angles must also be equal.
Two shapes are shown with no labels. Explain how you can tell which is the original and which is the image.
The image is the moved version — often shifted, flipped, or rotated from the original.
Explain how to find the line of reflection when you only have a figure and its reflected image.
The line of reflection is the perpendicular bisector of each point and its image.
Explain how the endpoint of a ray controls the direction it goes in real life.
The endpoint is the “start,” like a flashlight beam starting at the bulb.
Explain how to match the corresponding sides in two polygons, even if they look different.
Match sides by position and order — the first side of one shape matches the first side of the other.
Is the claim, “Perpendicular lines always make four right angles,” true? Explain what you think.
Yes, always true — perpendicular means exactly 90°, and linear pairs force all four angles to be 90°.
Explain why translations, reflections, and rotations all keep distances the same.
None of these transformations stretch or shrink the figure, so all distances stay the same.
Explain how to find the center of rotation using three pairs of matching points.
Draw segments between each point and its image; their perpendicular bisectors meet at the center.
Find the midpoint of a segment using two different methods and explain why both work.
Method 1: Midpoint formula
Method 2: Average the x‑values and y‑values Both work because the midpoint is halfway between the endpoints.
Explain how to use transformations to prove two triangles are congruent.
If one triangle can be mapped onto the other using only isometries, they are congruent.
You see a diagram with no angle measures. Explain how you can prove two lines are parallel using angle relationships only.
Show that corresponding or alternate interior angles are congruent. If they are, the lines must be parallel.
Describe how to figure out whether a transformation is a reflection, rotation, or translation.
Slides = translation
Flips = reflection
Turns = rotation
Explain why reflections keep distances the same by comparing points and their images.
Each point and its image are the same distance from the line of reflection.
Explain how to use a segment bisector to place something exactly between two objects.
A perpendicular bisector marks all points exactly in the middle.
Explain how to figure out which angles and sides match between two shapes in a diagram.
Look at the order of vertices and angle positions to match corresponding parts.
Explain how angle relationships prove they will stay parallel forever.
Make a transversal that forms equal corresponding angles with both roads. Equal corresponding angles guarantee parallel lines.
Find a sequence of transformations that maps triangle (1,2), (3,2), (2,4) onto (–4,1), (–2,1), (–3,3). Explain why your sequence works.
One correct sequence: translate left 5 and down 1, then reflect across the y‑axis.
Explain how to tell whether a shape was rotated or reflected when it’s not obvious.
If orientation reverses, it’s a reflection; if not, it’s a rotation.
Use the distance formula to prove two segments are congruent and explain why the method always works.
Use the distance formula on both segments; if the distances match, they’re congruent.
Write a step‑by‑step explanation showing two shapes that are congruent using transformations and angle relationships.
Translate, rotate, or reflect one shape to match the other; then show all sides and angles line up.