Geometry Chapter 7 Review Flashcards

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Questions and Answers

What does the Triangle Sum Theorem state?

The sum of the angle measures of a triangle is 180.

What is the sum of the angles in a triangle?

180

What is the sum of the angle measures in a quadrilateral?

360

What is the sum of the angles in a pentagon?

540 Signup and view all the answers

What is the sum of the angles in a hexagon?

720 Signup and view all the answers

What is the sum of the angles in a decagon?

1440 Signup and view all the answers

What does the Polygon Angle Sum Theorem state?

The sum = (n-2) X 180 Signup and view all the answers

What is an exterior angle?

An angle formed by one side of a polygon and the extension of an adjacent side. Signup and view all the answers

What is a remote interior angle?

An interior angle that is not adjacent to the exterior angle. Signup and view all the answers

What does the Triangle Inequality Theorem state?

The sum of any two side lengths of a triangle must be greater than the length of the third side. Signup and view all the answers

What does the Isosceles Triangle Theorem state?

If two sides of a triangle are congruent, then the two angles opposite the sides are congruent. Signup and view all the answers

What is an equilateral triangle?

A triangle with three congruent sides. Signup and view all the answers

What is an equiangular triangle?

A triangle with three congruent angles. Signup and view all the answers

What does the Equilateral Triangle Theorem state?

If a triangle is equilateral, then it is equiangular. Signup and view all the answers

What does the converse of the Equilateral Triangle Theorem state?

If a triangle is equiangular, then it is equilateral. Signup and view all the answers

What do side-angle relationships in triangles indicate?

If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. Signup and view all the answers

What does the Third Angle Theorem state?

If two angles are congruent, then the third angle must be congruent. Signup and view all the answers

Define Ratios in geometry.

A comparison of two quantities using division. Signup and view all the answers

What is a cross product?

The product of the extremes 'ad' and the product of the means 'bc'. Signup and view all the answers

What are extended ratios?

Ratios used to compare three or more quantities. Signup and view all the answers

What is a proportion?

An equation stating that two ratios are equal. Signup and view all the answers

What is a scale factor?

The ratio of the lengths of the corresponding sides of two similar polygons. Signup and view all the answers

What does Angle-Angle symmetry imply?

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Signup and view all the answers

What does Side-Side-Side symmetry imply?

If the corresponding side lengths of two triangles are proportional, then the triangles are similar. Signup and view all the answers

What does Side-Angle-Side symmetry imply?

If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. Signup and view all the answers

What is a triangle angle bisector?

An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides. Signup and view all the answers

What does Special Segmented Triangles altitude state?

If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of the corresponding sides. Signup and view all the answers

What does Special Segment Triangles median state?

If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides. Signup and view all the answers

What does Special Segment Triangle Angle Bisector state?

If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of the corresponding sides. Signup and view all the answers

What does the Triangle Proportionality Theorem state?

In any triangle, a line parallel to one side separates the other two sides proportionally. Signup and view all the answers

What does Proportional Parts With Parallel Lines imply?

When three or more parallel lines cut two transversals, they separate the transversals into proportional parts. Signup and view all the answers

Study Notes

Triangle Properties

Triangle Sum Theorem: The measure of interior angles in a triangle always adds up to 180 degrees.
Triangle Inequality Theorem: The sum of any two side lengths must be greater than the third side (e.g., AB + BC > AC).
Isosceles Triangle Theorem: If two sides of a triangle are congruent, the angles opposite those sides are also congruent.
Third Angle Theorem: If two angles are congruent, the third angle must also be congruent.

Polygon Angle Measures

Quadrilateral: Total interior angle measure is 360 degrees.
Pentagon: Total interior angle measure is 540 degrees.
Hexagon: Total interior angle measure is 720 degrees.
Decagon: Total interior angle measure is 1440 degrees.
Polygon Angle Sum Theorem: The sum of interior angles equals (n-2) × 180, where n is the number of sides.

Angles and Relationships

Exterior Angle: Formed by one side of a polygon and the extension of an adjacent side, and it forms a linear pair with the interior angle.
Remote Interior Angle: An interior angle not adjacent to a given exterior angle.

Triangle Classification

Equilateral Triangle: All sides and angles are congruent.
Equiangular Triangle: All angles are congruent.
Equilateral Triangle Theorem: An equilateral triangle is also equiangular, and vice versa.

Ratios and Proportional Relationships

Ratios: A comparison of two quantities, usually expressed in simplest form (a:b or a/b).
Cross Product: Refers to the product of the extreme terms and the product of the means in a proportion.
Proportion: An equation stating that two ratios are equal.
Scale Factor: The ratio of the lengths of corresponding sides of two similar polygons.

Similar Triangles Criteria

Angle-Angle (AA) Similarity: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
Side-Side-Side (SSS) Similarity: If corresponding sides of two triangles are proportional, the triangles are similar.
Side-Angle-Side (SAS) Similarity: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, the triangles are similar.

Special Segments in Triangles

Triangle Angle Bisector: An angle bisector divides the opposite side into segments proportional to the other two sides.
Triangle Proportionality Theorem: A line drawn parallel to one side of a triangle divides the other two sides proportionally.
Special Segmented Triangles: In similar triangles, the lengths of corresponding altitudes, medians, and angle bisectors are proportional to the lengths of their corresponding sides.
Parallel Lines: When three or more parallel lines cut through two transversals, they create proportional segments in the transversals.

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Test your knowledge of essential geometry concepts with these flashcards covering Chapter 7. Review key terms like the Triangle Sum Theorem and angle sums for polygons including triangles, quadrilaterals, pentagons, and more. Perfect for quick revision and enhancing your understanding of geometry basics.