Podcast
Questions and Answers
What are similar polygons?
What are similar polygons?
What happens during a similarity transformation?
What happens during a similarity transformation?
The pre-image and image are similar.
What are rigid transformations?
What are rigid transformations?
Rotations, reflections, and translations.
Similar polygons must have corresponding angles that are ________________.
Similar polygons must have corresponding angles that are ________________.
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Similar polygons must have ____________ side lengths that are proportional.
Similar polygons must have ____________ side lengths that are proportional.
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What does the similarity symbol look like?
What does the similarity symbol look like?
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What is a scale factor?
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
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?
What is the altitude of a triangle?
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What is the median of a triangle?
What is the median of a triangle?
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What is an angle bisector?
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 ____________.
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?
What is the pre-image?
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What is the image in transformations?
What is the image in transformations?
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What does a 'prime' notation represent in geometric transformations?
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.
Studying That Suits You
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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.
