Geometry, Unit 4: Triangle Similarity. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What does it mean for two triangles to be similar?
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Their corresponding angles are congruent and corresponding sides are proportional- What symbol represents similarity between two figures?
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~- What does AA (Angle-Angle) similarity state?
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If two angles of one triangle are congruent to two angles of another, the triangles are similar- What does SSS similarity state?
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If all three pairs of corresponding sides are proportional, the triangles are similar- What does SAS similarity state?
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If two pairs of sides are proportional and their included angles are congruent, the triangles are similar- What is a scale factor?
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The ratio of corresponding side lengths between two similar figures- What happens to a figure's area when its scale factor is k?
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The area is multiplied by k squared- What happens to a figure's perimeter when its scale factor is k?
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The perimeter is multiplied by k- What is the Triangle Proportionality Theorem?
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A line parallel to one side of a triangle divides the other two sides proportionally- What is the converse of the Triangle Proportionality Theorem used to prove?
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That a line is parallel to a triangle's side, if it divides the other two sides proportionally- What is the Side-Splitter Theorem, another name for a related concept?
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The Triangle Proportionality Theorem- What is an indirect measurement, using similar triangles?
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Using proportions from similar triangles to find a distance or height that is hard to measure directly- What real-world scenario commonly uses similar triangles for indirect measurement?
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Finding the height of a tall object using its shadow and a known reference- What is the Angle Bisector Theorem?
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An angle bisector in a triangle divides the opposite side into segments proportional to the other two sides- What is a midsegment of a triangle?
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A segment connecting the midpoints of two sides
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