3. If both pairs of opposite sides are parallel, tell...

3. If both pairs of opposite sides are parallel, tell whether each figure is a parallelogram, rectangle, rhombus, or square based on the information given. Use the most specific name possible. (Lesson 9.1, 9.3) (1/2 point each) a. b. c. d. 4. Can a square be called a rhombus? Explain why or why not. (Lesson 9.3) (1/2 point) 5. Examine quadrilateral FGHI below. In order to determine the length of each side of the parallelogram, which of the following equations would need to be used? Select two that apply. (Lesson 9.1) (1/2 point) G 8x - 6 H y + 10 11y F 9x I A. 8x - 6 = 9x B. 8x - 6 + 9x = 360 C. y + 10 = 11y D. y + 10 + 11y = 360 6. EFGH is a parallelogram. Find the given side length. (Lesson 9.1) (1/2 point each) a. EF b. EG 7y - 14 E F 12x + 10 15x + 7 J G H 2y + 21

Transcript

00:01 In question three, we're given that both pairs of opposite sides are parallel.

00:07 That directly means that all these shapes from a to d are parallelograms.

00:15 But well, we need to tell whether each of these figures is a parallelogram, rectangle, rumbus, or a square, based on the information that is given.

00:25 So because all of them are parallelograms, we're going to use the most specific name possible.

00:34 So let's start with a.

00:37 Now a is a parallelogram and it has a right angle.

00:42 So any parallelogram that has at least one right angle is considered to be a rectangle.

00:48 So a is a rectangle.

00:53 B is a parallelogram but also has one right angle so that makes it a rectangle and also it has a consecutive size of are congruent which makes it a rhombus and since it's both a rectangle and a rhombus then it qualifies to be a square c is a parallelogram but then we see that it has consecutive sides congruent so that makes it a rhombus d is a parallelogram but no consecutive sides are congruent so that makes it more just specifically a parallelogram.

01:46 Next, in question four, can a square be called a rhombus? and explain why or why not.

01:56 Now a square is always a rhombus.

02:05 A square is always a rhombus.

02:11 The reason why a square is always a rhombus is because a square is both a rectangle and a rhombus at any given point in time.

02:23 For a quadrilateral to qualify to be called a square, it must first be a rhombus, meaning all the sides of a square are congruent.

02:33 So a square can be called a rhombus.

02:37 But a square, sorry, a rhombus is sometimes a square, not all the time.

02:49 Okay, so not all rhombuses are square, just if they meet the criteria of also being rectangles or having one of the angles being right.

03:02 In question 5, we shall examine the quadrilateral f -g -h -i and then determine the right equation that will be used to find the length of each side of this parallelogram.

03:25 Now, in a parallelogram, the opposite sides are congruent, and therefore, gh is congruent to fi.

03:35 So we need to say that 8x minus 6 is equal to 9x.

03:39 So a is one of the equations that we would use to find that moans.

03:46 Also, gf is opposite hi, and they will, in a similar way, be congruent because in a parallelogram, opposite sides are congruent.

03:57 So the equation we're looking for is the equation y plus 10 equals 11y, which is c.

04:03 Now, b and d are not right, so we don't select those ones...

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