Math 3A

1

Chapter 5: Quadrilaterals Definition:

T

Q

S

R

Math 3A

2

Summary If 1. 2. 3. 4. Examples: Given parallelograms 12

1.

2. y

x

x

3y

50

45 70

35

33

2z - 3

K S

R

Prove: SJ ≅ QK

2

3.

1. ▱PQRS

P

1 J

Q

PJ ≅ RK

1. Given.

Math 3A

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Day 2 Proving Parallelograms Given: 1.

< Q ≅< S

2. QT ≅ RS

3. QT  RS

4.

< R ≅< T

5. QR ≅ ST

6. QR  ST

Prove: QRST is a parallelogram.

T

Q

S

R

Math 3A

4

Therefore, the 5 ways to prove that a quadrilateral is a parallelogram are: 1. 2. 3. 4. 5.

PROOFS A

1)

B 5

Prove: ABCD is a parallelogram

6

1. < 1 ≅< ADC

4 3

D

2

< 3 ≅< 5

1. Given

1

C

2) A

E

B

Prove: AEFD is a parallelogram D F

C

1. E is midpoint of AB F is midpoint of DC ABCD is a parallelogram

1. Given

Math 3A 3)

5 Prove: ABCD is a parallelogram

B

C

1. △ BOC ≅△ DOA

O

A

D

N

D

C

5

4)

2 4

3 1

A

6

M

B

Prove: AMCN is a parallelogram 1. ABCD is a parallelogram AN bisects < DAB

CM bisects < BCD < 5 ≅< 6

1. Given

1. Given

Math 3A

6

5)

D

C 4

1 E

F

3 2

A

Prove: AFCE is a parallelogram

1. ABCD is a parallelogram DE = BF

1. given

B

Math 3A

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Day 3 Parallel Lines

Given Triangle ABC:

A

1. Draw M, midpoint of AB 2. Draw N, midpoint of AC 3. What can you conclude about MN relative to BC ?

B The midsegment of a triangle is a segment that connects the midpoints of 2 sides of the triangle.

C

Math 3A 1. Given R, S and T are midpoints of the sides of ∆ABC. Complete the table

8 C

AB 12

a) b) c)

BC 14 15

AC 18 22

SR

TR

ST S

R 10

10

9

7.5 A

T

2. Given AR  BS  CT, RS ≅ ST R S

A B

T

C Complete: a) If RS = 12 then ST = ______

b) if AB = 8 then AC = ______

c) If AC = 20 then AB = ______

d) If AC = 10x then BC = ______

3. Given points X, Y and Z are the midpoints of AB, BC and AC. C

Y

X

A

a) b) c) d) e)

Z

B

If