PARALLELOGRAMS: RECTANGLES AND RHOMBUSES
Match the reasons with the statements given. Prove Theorem 4-22 (Hint: Show Triangle ADB is congruent to Triangle CDB.) Given: ABCD is a rhombus Prove: DB bisects ABC and ADC
1.ABCD is a rhombus 2.Triangle ADB congruent to Triangle CDB . 3.∠1 = ∠2, ∠3 = ∠4 4.DB bisects ∠ABC and ∠ADC 1. Given 2. Diagonals of parallelogram make congruent triangles. 3. CPCTE 4. Definition of angle bisector.
rhombus
A parallelogram with all sides equal.
rectangle
A parallelogram with four right angles.
trapezoid
A quadrilateral with at least one pair of parallel sides.
square
A rectangle with all sides equal and four right angles.
Which of the following best describe(s) the diagonals of a rectangle. Select all that apply. congruent perpendicular parallel intersecting
Congruent and Intersecting
THEOREM 4-20:
The diagonals of a rectangle are equal.
THEOREM 4-21:
The diagonals of a rhombus are perpendicular.
THEOREM 4-22:
Each diagonal of a rhombus bisects two angles of the rhombus.
Prove: The quadrilateral formed by joining in order the midpoints of the sides of a rectangle is a parallelogram. Given: ABCD is rectangle K, L, M, N are midpoints Prove: KLMN is a parallelogram. 1. ABCD is a rectangle K, L, M, N are midpoints 2. Draw diagonal AC 3. NM || AC NM = 1/2 AC KL || AC; KL = 1/2 AC 4. NM = KL 5. NM || KL 6. KLMN is a parallelogram 1. Given 2. Auxiliary Line 3. Midpoint segment of triangle is || to third side and = 1/2 third side 4. Substitution 5. Transitive 6. Which of the following reasons would complete the proof in line 6?
If a pair of opposite sides of a quadrilateral are parallel and equal, then it is a parallelogram.
Prove: If the four sides of a quadrilateral are equal, the quadrilateral is a rhombus. Given: AB = BC = CD = DA Prove: ABCD is rhombus 1. Ab = BC = CD = DA 2. ABCD is a parallelogram 3. ABCD is a rhombus 1. Given 2. 3. Definition of a rhombus Which of the following reasons completes the proof in line 2?
If both pairs of opposite sides are =, then a parallelogram.
