Questions and Answers
What is the ratio?
What is a proportion?
An equation stating that two ratios are equal.
What are cross products?
Can be found by multiplying the means and extremes.
What are extremes in a ratio?
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What are means in a ratio?
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What are similar polygons?
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What is the Similar Polygons Rule?
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What is a scale factor?
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What does proportionate mean?
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To show that 2 triangles are similar, show corresponding angles are __________.
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To show that 2 triangles are similar, show corresponding sides are __________.
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How to find distance?
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What are shortcuts for similar triangles?
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What does the AA similarity postulate state?
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What does the SSS similarity theorem state?
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What does the SAS similarity theorem state?
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What is The Triangle Proportionality Theorem?
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What is the converse of the triangle proportionality theorem?
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What is a midsegment?
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What is The Triangle Midsegment Theorem?
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What is The Proportional Perimeter Theorem?
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What is the special segments of similar triangles theorem?
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Study Notes
Ratios and Proportions
- Ratio: A comparison of two quantities expressed through division.
- Proportion: An equation that shows two ratios are equivalent.
- Cross Products: Calculated by multiplying the means and extremes in a proportion.
- Extremes: The first and last terms in a proportion.
- Means: The middle terms in a proportion.
Similar Polygons
- Similar Polygons: Polygons with the same shape, but potentially different sizes.
- Similar Polygons Rule: Two polygons are similar if their corresponding angles are congruent and corresponding sides are proportional.
- Scale Factor: The ratio comparing the lengths of corresponding sides in similar figures.
Triangle Similarity Criteria
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Similarity Criteria for Triangles:
- Show that corresponding angles are congruent.
- Show that corresponding sides are proportional.
- Write similarity statements.
- AA Similarity Postulate: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
- SSS Similarity Theorem: If all three pairs of corresponding sides are proportional, then the triangles are similar.
- SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, the triangles are similar.
Triangle Proportionality Theorems
- Triangle Proportionality Theorem: A line drawn parallel to the base of a triangle divides the legs into proportional segments.
- Converse of the Triangle Proportionality Theorem: If a line intersects the legs of a triangle in proportion, it is parallel to the triangle's base.
- Midsegment: A line connecting the midpoints of two sides of a triangle.
- Triangle Midsegment Theorem: The midsegment is parallel to the triangle's base and is half its length.
Perimeter and Special Segments
- Proportional Perimeter Theorem: Similar triangles have perimeters that are proportional to the lengths of their corresponding sides.
- Special Segments of Similar Triangles Theorem: Altitudes, bisectors, and medians in similar triangles are proportional to their corresponding sides.
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Description
This quiz explores the concepts of ratios, proportions, and their applications in similar polygons and triangles. Understand the definitions and rules that govern similarity, as well as how to identify and apply the AA similarity postulate. Test your knowledge with engaging questions on these important geometric concepts.