Questions and Answers
What are similar polygons?
What happens during a similarity transformation?
The pre-image and image are similar.
What are rigid transformations?
Rotations, reflections, and translations.
Similar polygons must have corresponding angles that are ________________.
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Similar polygons must have ____________ side lengths that are proportional.
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What does the similarity symbol look like?
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What is a scale factor?
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Theorem 7.1 states if two polygons are similar, then their _________________ are proportional to the scale factor between them.
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According to the Triangle Proportionality Theorem, if a line is __________________ to one side of a triangle and intersects the other two sides, it divides the sides into proportional lengths.
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The Converse of Triangle Proportionality Theorem states that if a line intersects two sides of a triangle and separates the sides _____________________ _______________ ___________, then the line is parallel to the third side of the triangle.
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What is the midsegment of a triangle?
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Triangle Midsegment Theorem states that a midsegment of a triangle is parallel to one side of the triangle and is ______ ______ the length of that side.
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There are ______ midsegments in a triangle.
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According to AA Similarity, if _________ angles in one triangle are congruent to two angles in another triangle, then the triangles are similar.
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For SSS Similarity, if the corresponding side lengths of two triangles are ____________________________, then the triangles are similar.
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For SAS Similarity, if the lengths of two sides of one triangle are proportional to two corresponding sides of another triangle and the ___________________ angles are congruent, then the triangles are similar.
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The Special Segments of Triangles Theorems state that if two triangles are similar, the lengths of corresponding ___________________, ____________________, and ___________________ are proportional.
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What is the altitude of a triangle?
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What is the median of a triangle?
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What is an angle bisector?
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According to the Angle Bisector Theorem, an angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two ____________.
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What is the pre-image?
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What is the image in transformations?
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What does a 'prime' notation represent in geometric transformations?
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Study Notes
Similar Polygons
- Similar polygons share the same shape but can differ in size.
- Corresponding angles in similar polygons are congruent.
- Corresponding side lengths in similar polygons are proportional.
Transformations
- Similarity transformation occurs when the pre-image and image are similar.
- Rigid transformations include rotations, reflections, and translations.
Scale Factor and Measurements
- The similarity symbol is represented by the tilde (~).
- Scale factor denotes the ratio of corresponding measurements of two similar figures.
Perimeters and Theorems
- Theorem 7.1 states that if two polygons are similar, their perimeters are proportional to the scale factor.
- The Triangle Proportionality Theorem asserts that a line parallel to one side of a triangle divides the other two sides into proportional lengths.
Triangle Properties
- The converse of the Triangle Proportionality Theorem states that if a line intersects two sides of a triangle and creates proportional corresponding segments, it is parallel to the third side.
- A midsegment joins the midpoints of two sides of a triangle.
- The Triangle Midsegment Theorem indicates that a midsegment is parallel to one side and measures one half the length of that side.
Triangle Similarity Criteria
- There are three midsegments in a triangle.
- AA Similarity: Two triangles are similar if two angles in one triangle are congruent to two angles in another.
- SSS Similarity: Triangles are similar if their corresponding side lengths are proportional.
- SAS Similarity: Triangles are similar if two sides are proportional and the included angles are congruent.
Special Segments
- In similar triangles, the lengths of corresponding altitudes, angle bisectors, and medians are proportional.
- The altitude is a perpendicular segment from a vertex to the opposite side of a triangle.
- A median connects a vertex to the midpoint of the opposite side.
- An angle bisector divides an angle into two congruent angles.
Bisector Theorem
- The Angle Bisector Theorem states that an angle bisector separates the opposite side into segments proportional to the lengths of the other sides.
Transformations
- A pre-image is the original shape or point prior to transformation.
- An image is the point or shape after transformation.
- A “prime” (A') designates point A after transformation.
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Description
Test your understanding of Chapter 7 vocabulary from Glencoe Geometry. This quiz covers key terms related to similar polygons and transformations crucial for mastering geometry concepts. Enhance your knowledge with these essential definitions.
