Similarity review games for Geometry.
This unit covers similar polygons, AA similarity and proportions in triangles — essential concepts for Geometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers similar polygons, AA similarity and proportions in triangles — essential concepts for Geometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Similar Polygons
Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. Students must be able to write a correct similarity statement, identify corresponding parts, and set up/solve proportions using the scale factor. The scale factor is the ratio of any pair of corresponding sides.
Key Points
- Corresponding angles are equal; corresponding sides have the same ratio (scale factor)
- The similarity statement order matters: ΔABC ~ ΔDEF means A↔D, B↔E, C↔F
- Scale factor k means sides of the larger figure = k × sides of the smaller figure
- Perimeters of similar figures share the same ratio as the sides; areas ratio is k²
Quadrilateral ABCD ~ Quadrilateral EFGH. AB = 6, EF = 9, and CD = 8. Find GH.
Set up the proportion using corresponding sides: AB/EF = CD/GH, which gives 6/9 = 8/GH. Cross-multiply to get 6·GH = 72, so GH = 12. The scale factor from ABCD to EFGH is 9/6 = 1.5, and 8 × 1.5 = 12 confirms the answer.
2 AA Similarity
Two triangles are similar if two pairs of corresponding angles are congruent (Angle-Angle Similarity). Because the angles of a triangle sum to 180°, knowing two angles are equal guarantees the third pair is also equal. Students must recognize AA setups in diagrams, including parallel lines and shared angles.
Key Points
- AA is the most commonly tested similarity shortcut — only two angles needed
- Shared (vertical) angles and angles formed by parallel lines (alternate interior, corresponding) are common AA triggers
- Once similarity is established, write a proportion using corresponding sides to find missing lengths
- Do NOT confuse AA similarity with SSS or SAS similarity — AA uses angles only
In the figure, DE ∥ BC. AD = 4, DB = 6, DE = 5. Find BC.
Because DE ∥ BC, angle ADE = angle ABC and angle AED = angle ACB (corresponding angles). This gives AA similarity, so ΔADE ~ ΔABC. The ratio of sides is AD/AB = 4/(4+6) = 4/10 = 2/5. Set up DE/BC = 2/5, so 5/BC = 2/5, giving BC = 12.5.
3 Proportions In Triangles
The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. Students must also know the Side-Splitter Theorem and the Angle Bisector Theorem for solving proportion problems on exams.
Key Points
- Triangle Proportionality Theorem: if DE ∥ BC, then AD/DB = AE/EC
- Angle Bisector Theorem: the bisector of an angle divides the opposite side in the ratio of the two adjacent sides
- Midsegment (midline) connects midpoints of two sides; it is parallel to the third side and half its length
- Always label which segments are being compared — a common error is setting up the ratio with the whole side instead of the partial segments
In ΔABC, ray BD bisects angle B. AB = 10, BC = 6, AC = 8. Find AD and DC.
By the Angle Bisector Theorem, AD/DC = AB/BC = 10/6 = 5/3. Since AD + DC = AC = 8, let AD = 5x and DC = 3x, so 5x + 3x = 8, giving x = 1. Therefore AD = 5 and DC = 3.
Questions, answered.
What is Similarity?
Similarity is Unit 7 of Geometry, covering similar polygons, AA similarity and proportions in triangles.
How to study for Geometry Unit 7?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.