Warm Up

Assessment 2GeometryAnswers

Warm Up # 11. “If a quadrilateral has four equal sides, then that

quadrilateral is a square.” Draw me a counterexample to the statement above?

2. Which of the following best describes the triangle below? Are they congruent? Similar?

3 36 6

35°

35°

Warm Up # 1B 1) Draw me 3 shapes that are similar but NOT

congruent? 2) Are these shape Similar? Congruent? a. b.

c. d.

Warm Up #2 1. A triangle has sides with lengths of 4 and 7 inches.

Which of the following could be the perimeter of the triangle?

2. A triangle has sides with lengths of 7 and 10 inches. Which of the following could be

the perimeter of the triangle?3. A triangle has sides with lengths of 11 and 17 inches.

Which of the following could be the perimeter of the triangle?

4 7

?

Warm Up #2B 1. A triangle has sides with lengths of 3 and 7 inches.

Which of the following could be the perimeter of the triangle?

2. A triangle has sides with lengths of 6 and 10 inches. Which of the following could be

the perimeter of the triangle?3. A triangle has sides with lengths of 10 and 17 inches.

Which of the following could be the perimeter of the triangle?

3 7

?

Warm Up # 3 1. What is the length of a side of the square below? a. b.

c. d.

5x + 60

6x + 43

5x + 13

3x + 43

8x + 13

4x + 43

5x + 15

x + 55

Warm Up # 3B1) In the triangles below, AB=DF and BC=EF.What additional information would be enough to

prove that triangle ABC and DEF are congruent?

B

A C D

E

F

Warm Up # 4 1. In the figure below,

a. If JK = LM, what will prove that JKL and JML are congruent?

b. If JM = KL, what will prove that JKL and JML are congruent?

J K

LM

13

24

Warm Up # 4B1) In the figure below, KL = JM. What postulate or theorem could be used to prove triangle

JKL = LMJ?

J

K

L

M

Warm Up # 5

1. A right triangle has legs of lengths 6 and 9. What is the length of the hypotenuse?

2. A right triangle has legs of lengths 8 and 12. What is the length of the hypotenuse?

3. A right triangle has legs of lengths 4 and 7. What is the length of the hypotenuse?

4. A right triangle has legs of lengths 11 and 13. What is the length of the hypotenuse?

Warm Up #5B

1. Which of the following statements would prove that ABCD is a rhombus?

2. What type of triangle is formed by the points A(2, 3), B(2, -3) and C(5, 0)?

3. What type of triangle is formed by the points A(–1, -1), B(2, -3) and C(5, 0)?

4. What type of triangle is formed by the points A(0, 5), B(2, 0) and C(0, 0)?

Warm Up #5C

1. If we have a parallelogram EFGH. Which of the following statements would prove that EFGH is a rhombus? Draw a Parallelogram, then a rhombus.

2. What type of triangle is formed by the points A(2, 4), B(2, -4) and C(5, 0)?

3. What type of triangle is formed by the points A(–1, -1), B(1, -3) and C(5, 0)?

4. What type of triangle is formed by the points A(0, 5), B(4, 0) and C(0, 0)?

Warm Up # 6• What additional information will be sufficient

to prove that triangle GFH and JFK are similar?Remember we just need 2 angle to be congruent to

have 2 similar triangles.

G

F

H

J

K

1

23

4 5

6

Warm Up # 6B In the triangle below, XY = MN and <X = < M.

1. Which additional information would be sufficient to prove that both triangle are congruent?

2. Which additional information would NOT be sufficient prove both triangle are congruent?

X Y

Z

MN

O

Warm Up # 7• A fence built around a field has the dimensions

shown below.1. What is the approximate length of the entire

fence?a. b. c.

3

5?

7

25?

10

26?

Warm Up # 7B1. What values of x and y make quadrilateral EFGH a

parallelogram? Hint : Opposite sides are congruent.

a. b. E F

GH

x – y

4x + y 26

4

E F

GH

3x + 4y

-x + 2y 2

24

Warm Up # 7C1. What values of x and y make quadrilateral EFGH a

parallelogram? Hint : Opposite sides are congruent.

a. b. E F

GH

x + y

2x + 3y 9

4

E F

GH

3x + 6

x + 2y 2

7y

Warm Up # 8If EFGH is a rhombus, solve for z? a. b.

E F

GH

(3, 4) (3+z, 4)

(0,0)(z,0)

E F

GH

(x, y) (x+z, y)

(0,0)(z,0)

Warm Up # 8BIf EFGH is a rhombus, solve for z? Then find Slope for

FH and EG? Then multiply FH and EG. a. What do you notice

about FH and EG?E F

GH

(3, 4) (3+z, 4)

(0,0)(z,0)

Warm Up # 8CIf EFGH is a rhombus, solve for z? Then find Slope for

FH and EG? Then multiply FH and EG. a. What do you notice

about FH and EG?E F

GH

(5, 12) (5+z, 12)

(0,0)(z,0)

Warm Up # 9 If EFGH is a parallelogram, what are the

coordinates of point E?a. b.

E F

GH

(?, ?) (6, 4)

(0,0)(5,0)

E F

GH

(?, ?) (y, z)

(0,0)(x,0)

Warm Up # 9B1. Which of the following facts would prove that

EFGH and LMNO are similar?

Hint: What should the ratio be for FG/MO, HG/NO ?What should <H and <G be congruent to ? If we have 2 parallel lines would it help? Which two?

E F

GH

L M

N O

115 105115 1059

6

3

2

Warm Up # 10 Page 2271.Make a segment AB. 2.Put the tip of the compass on point A.3.Open the pencil(with compass) tip so that it extend

past point B. Then Draw an Arc.4.Without adjusting the width of the compass, place

the tip on point B and draw an arc that intersects the first arc at point C.

5.Draw a line segment from point A to C and from point B to C.

Warm Up # 10B Page 2711. On a triangle ABC. Put the tip of the compass on to

point B. 2.Open the pencil (with compass) tip so that it not

pass segment AC. Draw an arc. Label the intersection on BC point K and on AB point M.

3.Without adjusting the width of the compass. Place the tip on point K and draw an arc. Same with point M.

4.Where both arc intersects call it point H. 5.Lastly, make segment BH and that is the altitude.

1. Find the area for Triangle x.2. Find the area for Triangle y.3. Find the area for Triangle z.4. Find the area of x , y , z.5. Find area of the trapezoid.6. Find sum for triangle x, y, z.7. Does answer number 6 have the same answer as number 5?

Warm-Up 10 C: Page 545: Pythagorean Theorem Proof.

22

4

3

3

4

5

5

xx

yy

zz

1. Find the area for Triangle x.2. Find the area for Triangle y.3. Find the area for Triangle z.4. Find the area of x , y , z.5. Find area of the trapezoid.6. Find sum for triangle x, y, z.7. What happens when the Answer of problem 5 is equal to Answer of problem 6?

Warm-Up 10 D: Page 545: Pythagorean Theorem Proof.

22

j

k

k

j

m

m

xx

yy

zz

Warm Up # 111. Which of the following is not an undefined term use in geometry?

a. Triangle b. point c. line d. plane

2. Which of the following statements represents deductive reasoning? a. Using logic to draw conclusions based on accepted statements. b. Recognizing pattern in weather, then making a prediction based

upon that pattern.c. Singing “Yankee Doodle Dandy” to yourself.d. Clark Gable

3. Which of the following statements represents inductive reasoning?a. Using logic to draw conclusions based on accepted statements. b. Recognizing a pattern in weather, then making a prediction

based upon that pattern. c. Reciting a Dr. Seus phrase to your neighbor. d. Elvis Grabac.