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?
- Their corresponding angles are congruent and corresponding sides are proportional
- What symbol represents similarity between two figures?
- ~
- What does AA (Angle-Angle) similarity state?
- If two angles of one triangle are congruent to two angles of another, the triangles are similar
- What does SSS similarity state?
- If all three pairs of corresponding sides are proportional, the triangles are similar
- What does SAS similarity state?
- If two pairs of sides are proportional and their included angles are congruent, the triangles are similar
- What is a scale factor?
- The ratio of corresponding side lengths between two similar figures
- What happens to a figure's area when its scale factor is k?
- The area is multiplied by k squared
- What happens to a figure's perimeter when its scale factor is k?
- The perimeter is multiplied by k
- What is the Triangle Proportionality Theorem?
- 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?
- 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?
- The Triangle Proportionality Theorem
- What is an indirect measurement, using similar triangles?
- 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?
- Finding the height of a tall object using its shadow and a known reference
- What is the Angle Bisector Theorem?
- 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?
- A segment connecting the midpoints of two sides
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