Polygons & Quadrilaterals Name: ID Homework 4: Rectangles Date: Per: This is a 2-page documenf! Directions: If each quadrilateral below is a rectanale, find fhe missing measures 1. GF 2. D 11 E VW= GE = W WX= DF= 19 YW HF= Z ZX DG= X Y 31 VX F G GH= 14 3. m9 m/5 m/1 Spe m210 m/2 m/6 m7 m11 71 m/3 6 m8 mL4 5. 126 M D L ? m/BCD m/ABD mLADE mZAEB mJMK m/HJ L MJKH m/LHK m4CBE m/DEA m/HLK mJLK 6. Find WZ 7. If SQ 11x-26 and PR 5x+ 28, find PR. 7x-6 3r+ 14 S Y Gina Wson (Al Things Algebra. LLC). 2014-2019 LIH 15x+ 19 and ON=10x + 2. find PN 9. If LO AE 6x-55 and EC 3x- 16, find DR E D 10. If DE 4x+ 1. EB= 12x-31, and CD 28, find AD, C 12. Find mLADE 11. Find m2GJK (4x+15 B G (Sx+8 H (13x+7) D (7?- 16y 13. Find mZVWz 14. Find mLDHG D (9x+3) E ? (5x-12) Y ? (2x-3) G (14x-27) Gina Wilson (Al Things Algebro. LLC). 2014-2019
The Correct Answer and Explanation is :
It seems you’re working with a set of geometry problems involving quadrilaterals, specifically rectangles. Let’s break down and address some of the key problems. I’ll provide explanations for each part.
- Finding Missing Measures in Rectangles
Rectangles have certain properties:
- Opposite sides are equal.
- All angles are 90 degrees. If you’re given a rectangle and asked to find missing side lengths, use these properties. For instance:
- If you know one side (say, the length of side GF) and another side (say, WX), you can use the fact that opposite sides are equal to find the missing sides. For example, if GF = WX, then you can substitute that into your equations to solve for the missing measurements.
- Angles of a Rectangle
In a rectangle, the four angles are all right angles (90°). If the problem involves calculating angles, you can assume that every interior angle is 90°. If you have angles expressed algebraically, like ( m \angle ABC ) or ( m \angle XYZ ), use algebraic expressions to solve for each. - Algebraic Expressions for Sides and Angles
Several of the questions involve solving equations for unknown values of side lengths or angles using algebraic expressions. Here’s a general approach to solving them:
- Example 1: If ( m \angle ABC = 2x + 3 ) and ( m \angle ABC = 90^\circ ), you can set the equation:
[
2x + 3 = 90
]
Solve for ( x ) by subtracting 3 from both sides:
[
2x = 87
]
Then, divide both sides by 2 to find ( x = 43.5 ). - Example 2: If you’re given two expressions for the sides of a rectangle, like ( SQ = 11x – 26 ) and ( PR = 5x + 28 ), and you know ( SQ = PR ) (since opposite sides of a rectangle are equal), set up the equation:
[
11x – 26 = 5x + 28
]
Solve this by first subtracting ( 5x ) from both sides:
[
6x – 26 = 28
]
Then, add 26 to both sides:
[
6x = 54
]
Finally, divide by 6:
[
x = 9
]
Now substitute ( x = 9 ) back into either expression for ( SQ ) or ( PR ) to find their values.
- Final Steps and Calculations
After solving for ( x ), substitute the value back into any equations where you’re given side lengths or angles in terms of ( x ). Once you do this for all the unknowns, you’ll have the values for all sides and angles.
In summary, the key steps are:
- Recognizing the properties of rectangles (opposite sides are equal, angles are 90°).
- Setting up algebraic equations for missing values.
- Solving the equations and substituting the solutions back into the original equations.
These steps should help guide you through your problems. Let me know if you’d like to go through any specific problem in more detail!