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Questions and Answers
What is Theorem 6.1 about the interior angles of an n-gon?
What is Theorem 6.1 about the interior angles of an n-gon?
- The sum of the measures of the interior angles of an n-gon is (n-2) x 180 (correct)
- The diagonals of a parallelogram bisect each other
- The sum of the measures of opposite angles in a quadrilateral is supplementary
- The sum of the measures of exterior angles of a polygon is 360 degrees
What does Theorem 6.2 state about exterior angles of a polygon?
What does Theorem 6.2 state about exterior angles of a polygon?
- The exterior angles of a parallelogram are equal
- Exterior angles have no relation to quadrilaterals
- The sum of the measures of exterior angles, one at each vertex, is 360 degrees (correct)
- The sum of the measures of exterior angles is 180 degrees
According to Theorem 6.3, what is true if a quadrilateral is a parallelogram?
According to Theorem 6.3, what is true if a quadrilateral is a parallelogram?
- Its opposite sides are congruent (correct)
- It has equal angles
- Its consecutive angles are supplementary
- All angles are right angles
What does Theorem 6.4 state about the angles of a parallelogram?
What does Theorem 6.4 state about the angles of a parallelogram?
If a quadrilateral is a parallelogram, what does Theorem 6.5 say about its opposite angles?
If a quadrilateral is a parallelogram, what does Theorem 6.5 say about its opposite angles?
According to Theorem 6.6, what happens to the diagonals of a parallelogram?
According to Theorem 6.6, what happens to the diagonals of a parallelogram?
What does Theorem 6.7 say about parallel lines and traversals?
What does Theorem 6.7 say about parallel lines and traversals?
What conclusion can be drawn from Theorem 6.8 regarding opposite sides of a quadrilateral?
What conclusion can be drawn from Theorem 6.8 regarding opposite sides of a quadrilateral?
According to Theorem 6.9, under what condition is a quadrilateral a parallelogram?
According to Theorem 6.9, under what condition is a quadrilateral a parallelogram?
What does Theorem 6.10 state about opposite angles in a quadrilateral?
What does Theorem 6.10 state about opposite angles in a quadrilateral?
What conclusion does Theorem 6.11 draw from the bisecting diagonals of a quadrilateral?
What conclusion does Theorem 6.11 draw from the bisecting diagonals of a quadrilateral?
According to Theorem 6.12, what is true if one pair of opposite sides of a quadrilateral is both congruent and parallel?
According to Theorem 6.12, what is true if one pair of opposite sides of a quadrilateral is both congruent and parallel?
What does Theorem 6.13 state about the diagonals of a rhombus?
What does Theorem 6.13 state about the diagonals of a rhombus?
What is true according to Theorem 6.14 about the diagonals of a rhombus?
What is true according to Theorem 6.14 about the diagonals of a rhombus?
According to Theorem 6.15, what is true about the diagonals of a rectangle?
According to Theorem 6.15, what is true about the diagonals of a rectangle?
What does Theorem 6.16 state regarding the diagonals of a parallelogram?
What does Theorem 6.16 state regarding the diagonals of a parallelogram?
According to Theorem 6.17, what conclusion can be drawn if one diagonal of a parallelogram bisects a pair of opposite angles?
According to Theorem 6.17, what conclusion can be drawn if one diagonal of a parallelogram bisects a pair of opposite angles?
What does Theorem 6.18 say about the congruence of diagonals in a parallelogram?
What does Theorem 6.18 say about the congruence of diagonals in a parallelogram?
According to Theorem 6.19, what is true about an isosceles trapezoid?
According to Theorem 6.19, what is true about an isosceles trapezoid?
What does Theorem 6.20 state about the diagonals of an isosceles trapezoid?
What does Theorem 6.20 state about the diagonals of an isosceles trapezoid?
According to Theorem 6.21, what can be stated about a trapezoid's midsegment?
According to Theorem 6.21, what can be stated about a trapezoid's midsegment?
What conclusion does Theorem 6.22 draw concerning the diagonals of a kite?
What conclusion does Theorem 6.22 draw concerning the diagonals of a kite?
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Study Notes
Interior and Exterior Angles of Polygons
- The sum of the measures of the interior angles of an n-gon is given by the formula ((n-2) \times 180).
- The sum of the measures of exterior angles of a polygon, with one angle at each vertex, is always 360 degrees.
Properties of Parallelograms
- Opposite sides of a parallelogram are congruent.
- Consecutive angles in a parallelogram are supplementary (sum to 180 degrees).
- Opposite angles in a parallelogram are congruent.
- Diagonals of a parallelogram bisect each other.
Testing for Parallelograms
- If both pairs of opposite sides of a quadrilateral are congruent, it is a parallelogram.
- If one angle of a quadrilateral is supplementary to both of its consecutive angles, it will also be a parallelogram.
- If both pairs of opposite angles of a quadrilateral are congruent, it confirms the shape is a parallelogram.
- If the diagonals of a quadrilateral bisect each other, it indicates the quadrilateral is a parallelogram.
- A quadrilateral is a parallelogram if one pair of opposite sides is both congruent and parallel.
Special Types of Parallelograms
- In a rhombus, diagonals are perpendicular to each other.
- Each diagonal of a rhombus bisects a pair of opposite angles.
- A rectangle has congruent diagonals.
Properties of Rhombuses and Rectangles
- If the diagonals of a parallelogram are perpendicular, it is classified as a rhombus.
- If one diagonal of a parallelogram bisects a pair of opposite angles, it is a rhombus.
- If the diagonals of a parallelogram are congruent, it confirms the shape is a rectangle.
Properties of Trapezoids and Isosceles Trapezoids
- In an isosceles trapezoid, each pair of base angles is congruent.
- The diagonals of an isosceles trapezoid are congruent.
- For a trapezoid, the midsegment is parallel to the bases and its length equals half the sum of the lengths of the bases.
Properties of Kites
- The diagonals of a kite intersect at right angles (are perpendicular).
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