Geometry B U2 L6 Trapezoids and Kites Quiz Answers -

1. Classify the figure in as many ways as possible.
Answer - A. rectangle; square; quadrilateral; parallelogram; rhombus

2. Which statement is true?
Answer - C. All rectangles are quadrilaterals.

3. Lucinda wants to build a square sandbox, but she has no way of measuring angles. Which of the following explains how she can make sure the sandbox is square by measuring only length.
Answer - B. Arrange four equal-lengths, so the diagonals are equal lengths also.

4. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 20x + 9 and m∠M = 14x + 15, find m∠K.
Answer - A. 151°

5. In the rhombus m∠1 = 18x, m∠2 = x + y, and m∠3 = 30z. Find the value of x + y + x. The diagram is not drawn to scale.
Answer - A. 93

6. In rectangle KLMN, KM = 6x + 16, and LN = 49. Find the value of x.
Answer - D. 5.5

7. Find the value of a. The diagram is not to scale.
Answer - B. 144°

8. LM is the midsegment of trapezoid ABCD. If AB = 46 and DC = 125, what is LM?
Answer - D. 85.5

9. ABCD is a rhombus. Explain why ABC=CDA.
Answer - All sides of the rhombus have equal length, so AB is congruent to AD, and BC is congruent to DC, BD is congruent to BD by reflexive equality. ABC is therefore congruent to CDA by SSS.

100% Hope this helps!

Does anyone have part two answers?

100% 👍

1. Well, isn't that figure just a jack of all trades! It can be classified as a rectangle, square, quadrilateral, parallelogram, and rhombus. It's got more identities than a secret agent!

2. Let me give you some rectangles of wisdom: Yes, it's true, all rectangles are quadrilaterals. Just like all clowns wear big shoes, it's a defining feature!

3. Lucinda is thinking outside the sandbox here! If she wants to build a square sandbox without measuring angles, she can simply make sure all four sides are equal in length, and voila, the diagonals will also be equal. Who needs angles when you've got equal lengths?

4. Ah, the bases are loaded with angles! If the base angles of that isosceles trapezoid are m∠J = 20x + 9 and m∠M = 14x + 15, then the missing angle m∠K can be found by turning on the mathomatics. And the answer is... drum roll, please... 151°! That angle just aced the test!

5. Oh, the rhombus has some angle shenanigans going on! If m∠1 = 18x, m∠2 = x + y, and m∠3 = 30z, then the value of x + y + x is... wait for it... 93! It's like solving a puzzle with angles and variables, but don't worry, I got your back!

6. Time to unlock the mystery of x in rectangle KLMN! If KM = 6x + 16 and LN = 49, then the value of x is... ta-da... 5.5! You see, my friend, it's all about applying some mathematical clown magic.

7. The value of a in the diagram is shouting at me, it's saying: "Hey clown, I'm 144°!" So, there you have it, the angle revealed itself! It must love the spotlight!

8. LM, the midsegment of trapezoid ABCD, is eager to reveal its length! If AB = 46 and DC = 125, then the length of LM is none other than 85.5! It's the happy medium between the two bases. You can count on me for midsegment measurements!

9. Ah, the rhombus and its symmetrical ways! ABC is congruent to CDA because all sides of the rhombus are equal in length. You can't argue with symmetry, my friend! It's the secret language of shapes.

Hope my humorous explanations brought a smile to your face while solving those geometry wonders!

Great job on completing the quiz! Here's how you can find the answers to each question:

1. To classify the figure in as many ways as possible, you need to identify the properties or characteristics of the figure. In this case, the figure can be classified as a rectangle because it has four right angles, a square because it has four equal sides and four right angles, a quadrilateral because it has four sides, a parallelogram because opposite sides are parallel, and a rhombus because opposite sides are parallel and all sides are congruent.

2. To determine which statement is true, you need to understand the definitions and relationships between different geometric shapes. In this case, the statement "All rectangles are quadrilaterals" is true because a rectangle is a quadrilateral by definition.

3. To help Lucinda ensure that the sandbox is square by measuring only length, the key is to focus on the diagonals of a square. The diagonals of a square are equal in length and bisect each other at right angles. So, by arranging four equal-length sides so that the diagonals are also equal in length, Lucinda can ensure that the sandbox is square.

4. To find the measure of angle K in isosceles trapezoid JKLM, you need to use the properties of isosceles trapezoids. In an isosceles trapezoid, the base angles (angles at the bases) are congruent. Given the measures of angles J and M, you can set them equal to each other and solve for x. Once you find the value of x, you can substitute it into either angle J or M to find their measures. Finally, since angles J, K, and M are consecutive angles in a quadrilateral, the sum of their measures is 360 degrees. By subtracting the measures of angles J and M from 360 degrees, you can find the measure of angle K.

5. To find the value of x + y + x in the given rhombus, you need to use the properties of rhombuses. In a rhombus, opposite angles are congruent. Given the measures of angles 1, 2, and 3, you can set up equations to find the values of x, y, and z. Finally, substitute the found values of x and y into the expression x + y + x to calculate the answer.

6. To find the value of x in rectangle KLMN, you need to use the information provided. The length of a rectangle is represented by the side KM, and it is given as 6x + 16. The width of a rectangle is represented by the side LN, and it is given as 49. Set up an equation with the length and width expressions, and solve for x.

7. To find the value of angle a in the given diagram, you need to consider the properties of opposite angles and supplementary angles. Since angle a and angle 144 are opposite angles, they are congruent. Additionally, the sum of angles a and 144 is 180 degrees because they are supplementary. Set up an equation and solve for a.

8. To find the value of LM, which is the midsegment of trapezoid ABCD, you need to use the definition of a midsegment. In a trapezoid, the midsegment is the segment that connects the midpoints of the two non-parallel sides. So, LM is equal to half of the sum of AB and DC. Substitute the given values and calculate the answer.

9. To explain why ABC = CDA in rhombus ABCD, you can use the properties of rhombuses. In a rhombus, opposite angles are congruent. Since ABCD is a rhombus, angles ABC and CDA are opposite angles, and therefore, they are congruent.

All correct, the final question doesn't specify how many reasons there should be to define the congruence between the triangles. Goodluck!