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Chapter 10: Quadrilaterals
Topic 2: Rectangles
Do Now: In parallelogram ๐ด๐ต๐ถ๐ท, the measures of angles ๐ด and ๐ต are in the ratio of 1:8. Find ๐ < ๐ด and ๐ < ๐ต.
Rectangles
- A rectangle is a parallelogram that has one right angle. Diagram: Properties:
๏ท All the properties of a parallelogram.
๏ท One right angle. (All angles are right angles).
๏ท Diagonals are congruent.
Word Problems:
ABCD is a rectangle. Diagonal AC measures 2x + 3 and diagonal BD measures 4x - 21. Find the value of x and the measure of AC and BD.
In rectangle ABCD, the diagonals AC and BD intersect at point E. If the measure of AE = 5, find the length of EC, AC, and BD.
In rectangle ABCD, diagonals AC and BD meet at point E. If CB=6, AB = 8, and AC = 10, find AD, CD, EC, AE, DE, EB, and DB.
In rectangle QRST, diagonals QS and RT meet at point U. If the measure of QU=3x+4 and US = x + 20, what is the value of x? Find QU, US, QS, RU, UT, and RT.
In rectangle PQRS, diagonal PR=4x + 3 and diagonal QS=6x-7. What is the length of diagonal QS?
Given the following diagram, solve for the value of ๐ฅ. Find the length of ๐ต๐ถ.
The diagonals of a rectangle ๐
๐๐๐ intersect at ๐. If ๐๐ = 3๐ฅ โ 3 and ๐
๐ = 5๐ฅ โ 1, find the value of ๐ฅ.
In rectangle ๐ด๐ต๐ถ๐ท, ๐ต๐ถ = 30 and ๐ด๐ต = 40. If the diagonals ๐ด๐ถฬ
ฬ
ฬ
ฬ
and ๐ต๐ทฬ
ฬ
ฬ
ฬ
intersect at ๐ธ, find the measure of ๐ต๐ธฬ
ฬ
ฬ
ฬ
. (Hint: First find the length of a diagonal).
Review Section: _____ 16) The measure of five of the interior angles of a hexagon are 150, 100, 80, 165, and 150. What is the measure of the sixth interior angle? (1) 75 (2) 80 (3) 105 (4) 180
_____ 17) The x-axis is not the line of reflection for which of the following pairs of points? (1) ๐
(1, 5) โ ๐
โฒ(1, โ5)^ (2) ๐ด(โ2, โ4) โ ๐ดโฒ(โ2, 4) (3) ๐ท(โ9, 4) โ ๐ทโฒ(9, โ4) (4) ๐น(3, โ2) โ ๐นโฒ(3, 2)
_____ 18) In parallelogram ABCD shown, diagonals AC and BD intersect at E. Which statement must be true? (1) ๐ด๐ถ โ
๐ท๐ต (2) < ๐ด๐ต๐ท โ
< ๐ถ๐ต๐ท (3) โ๐ด๐ธ๐ท โ
โ๐ถ๐ธ๐ต (4) โ๐ท๐ถ๐ธ โ
โ๐ต๐ถ๐ธ
- A regular pyramid has a height of 12 cm. and a square base. If the volume of the pyramid is 256๐๐^3 , how many centimeters are in the length of one side of its base? The volume of a pyramid can be represented by the formula: ๐ = 13 ๐ตโ, as seen on the reference sheet.
