Questions and Answers
Opposite sides of a rectangle are parallel.
Adjacent sides of a rhombus are congruent.
Diagonals of a rhombus are congruent.
Opposite sides of a parallelogram are congruent.
Signup and view all the answers
Diagonals of a rectangle are perpendicular.
Signup and view all the answers
Diagonals of a rectangle bisect opposite angles.
Signup and view all the answers
Opposite angles of a parallelogram are congruent.
Signup and view all the answers
Consecutive angles of a parallelogram are congruent.
Signup and view all the answers
Diagonals of a parallelogram bisect each other.
Signup and view all the answers
The four angles of a rhombus are right angles.
Signup and view all the answers
Consecutive sides of a rhombus are congruent.
Signup and view all the answers
The diagonals of a quadrilateral bisect each other.
Signup and view all the answers
If the measure of two angles of a quadrilateral are equal, then the quadrilateral is a parallelogram.
Signup and view all the answers
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Signup and view all the answers
To prove that a quadrilateral is a parallelogram, it is sufficient to show that one pair of opposite sides is parallel.
Signup and view all the answers
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Signup and view all the answers
A square is a rhombus.
Signup and view all the answers
A quadrilateral is a parallelogram.
Signup and view all the answers
A rectangle is a rhombus.
Signup and view all the answers
A parallelogram with at least one right angle is a square.
Signup and view all the answers
A trapezoid is a parallelogram.
Signup and view all the answers
A quadrilateral is a trapezoid.
Signup and view all the answers
The bases of an isosceles trapezoid are congruent.
Signup and view all the answers
A parallelogram is a rectangle.
Signup and view all the answers
A kite has congruent diagonals.
Signup and view all the answers
Each diagonal of a parallelogram divides it into two congruent triangles.
Signup and view all the answers
A parallelogram whose diagonals are congruent and perpendicular to each other is a square.
Signup and view all the answers
A quadrilateral is a parallelogram if its diagonals are perpendicular.
Signup and view all the answers
The bases of a trapezoid are congruent.
Signup and view all the answers
Opposite angles of a parallelogram are supplementary.
Signup and view all the answers
If the diagonals of a quadrilateral are perpendicular to each other, the quadrilateral is a square.
Signup and view all the answers
A diagonal of an isosceles trapezoid divides it into two congruent triangles.
Signup and view all the answers
A rhombus is equiangular.
Signup and view all the answers
A quadrilateral whose angles are congruent is a rectangle.
Signup and view all the answers
If the diagonals of a square are drawn, then the resulting four triangles are isosceles right triangles.
Signup and view all the answers
If the diagonals of a parallelogram bisect opposite angles, the parallelogram is a square.
Signup and view all the answers
Study Notes
Key Properties of Quadrilaterals
- Opposite sides of a rectangle are always parallel.
- Adjacent sides of a rhombus are always congruent.
- Diagonals of a rhombus are sometimes congruent.
- Opposite sides of a parallelogram are always congruent.
- Diagonals of a rectangle are sometimes perpendicular.
- Diagonals of a rectangle always bisect opposite angles.
- Opposite angles of a parallelogram are sometimes congruent.
- Consecutive angles of a parallelogram are sometimes congruent.
- Diagonals of a parallelogram always bisect each other.
- The four angles of a rhombus are sometimes right angles.
- Consecutive sides of a rhombus are always congruent.
Quadrilaterals and Parallelograms
- Diagonals of a quadrilateral sometimes bisect each other.
- If two angles of a quadrilateral are equal, the quadrilateral is sometimes a parallelogram.
- If both pairs of opposite sides of a quadrilateral are congruent, it is always a parallelogram.
- A sufficient condition to prove a quadrilateral is a parallelogram is never achieved by showing one pair of opposite sides is parallel.
- If both pairs of opposite angles of a quadrilateral are congruent, it is always a parallelogram.
Special Quadrilaterals
- A square is always a rhombus.
- A quadrilateral is sometimes a parallelogram.
- A rectangle is sometimes a rhombus.
- A parallelogram with at least one right angle is sometimes a square.
- A trapezoid is never a parallelogram.
- A quadrilateral is sometimes a trapezoid.
- The bases of an isosceles trapezoid are never congruent.
- A parallelogram is sometimes a rectangle.
- A kite has congruent diagonals never.
Triangle Properties in Quadrilaterals
- Each diagonal of a parallelogram always divides it into two congruent triangles.
- A parallelogram whose diagonals are congruent and perpendicular to each other is always a square.
- A quadrilateral can sometimes be a parallelogram if its diagonals are perpendicular.
- The bases of a trapezoid are never congruent.
- Opposite angles of a parallelogram are sometimes supplementary.
- If the diagonals of a quadrilateral are perpendicular, the quadrilateral is sometimes a square.
- A diagonal of an isosceles trapezoid never divides it into two congruent triangles.
- A rhombus is sometimes equiangular.
- A quadrilateral with congruent angles is always a rectangle.
- If the diagonals of a square are drawn, the resulting four triangles are always isosceles right triangles.
- If the diagonals of a parallelogram bisect opposite angles, the parallelogram is sometimes a square.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on the unique properties of various quadrilaterals, including rectangles, rhombuses, and parallelograms. This quiz will challenge your understanding of sides, angles, and diagonals in these geometric shapes.
