Congruent Figures With Algebraic Side Lengths
Written by Adi Ackerman, Head Teacher
"Congruent Figures With Algebraic Side Lengths" is written for 8th Grade (Ages 13-14). A 7th grader who is already steady on transformations can use it too, and an older student can use it as a short review.
8th grade math worksheet: write and solve equations from matching sides of congruent figures, such as 2x + 3 and 3x − 6. Answer key included. Part of our congruence and similarity transformations collection.
How do I use this worksheet?
Start with What Rigid Motions Preserve so students see why rigid motions make congruent figures. Move to the sequence and similarity grids, then close with the angle-angle sheets.
What students will practice
- Students will use a congruence statement to match sides of two figures.
- Students will write and solve an equation for x from a pair of equal sides.
- Students will find side lengths in centimeters once x is known.
Translate Figures on the Coordinate Plane
Rotate Figures About the Origin
Reflect Figures Across the Axes and Lines
Dilate Figures From the Origin
Describe Translations With Coordinate Rules
Describe Rotations From Before and After Graphs
Describe Reflections and Name the Line
Describe Dilations and Find the Scale Factor
Curriculum Links
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FAQ
How do I use this congruence and similarity worksheet?
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Start with What Rigid Motions Preserve so students see why rigid motions make congruent figures. Move to the sequence and similarity grids, then close with the angle-angle sheets.
What does this worksheet teach?
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Write and solve equations from matching sides of congruent figures, such as 2x + 3 and 3x − 6. The directions on the page read: Each pair of figures is congruent, so matching parts are equal. Write and solve an equation for x. Then find each measure. Lengths are in centimeters. An answer key is included.
Can I use this congruence and similarity worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade transformations, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
What do rigid motions preserve?
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Translations, reflections and rotations keep side lengths and angle measures the same, so the image is congruent to the original. What Rigid Motions Preserve has students measure a trapezoid and its image to check.
What is angle-angle similarity?
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If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The third angles must then match too, because each triangle's angles add up to 180°.
How do you find a missing side in similar triangles?
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Match the corresponding sides, write a proportion and solve for x. Use Angle-Angle Similarity to Find Missing Sides first asks which two pairs of angles make the triangles similar.
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Worksheet Details
| Grade | 8th Grade |
| Subject | Math |
| Topic | Transformations |
| Pages | 1 page |
| Difficulty | Medium |
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Translate Figures on the Coordinate Plane
Rotate Figures About the Origin
Reflect Figures Across the Axes and Lines
Dilate Figures From the Origin
Describe Translations With Coordinate Rules
Describe Rotations From Before and After Graphs
Describe Reflections and Name the Line
Describe Dilations and Find the Scale Factor