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Statements

Reasons

𝑆𝑞𝑢𝑎𝑟𝑒 𝐴𝐵𝐶𝑆≅ 𝑆𝑞𝑢𝑎𝑟𝑒𝐸𝐹𝐺𝑆1. Given2. 2. Corresponding parts of congruent figures are congruent

9. ESR 9.

3. 3. Reflexive

7. 4 7. All right angles are congruent

31 24

5. are supplements are supplements 5. Angles on a line 4. 2 are right angles 4. Squares contain right four right angles 6. 4 are right angles 6. Supplements of right angles are right angles 8. ESR are right triangles 8. A triangle that contains a right angle is a right triangle

I I

X

UNIT 3Lesson 10 – Mid-segment of a

Triangle

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Statements

Reasons

1. 1. Given2. 2. Opposite sides of a rectangle are congruent

6. 6. 7. CPCTC7.

3. and are right angles 3. A rectangle contains four right angles 4. 4. All right angles are congruent5. 5. A midpoint divides a segment into two congruent segments 8. 8. An isosceles triangle has two congruent sides

I I

II II

III III

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𝑋+4=15−4−4𝑋=11

𝐶𝐷=15𝐴𝐷=3 (11)+2=35𝐶𝐵=35

𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=15+15+35+35𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=100

Opposite sides of a parallelogram are congruent

Opposite sides of a parallelogram are congruent

Substitution postulate

Substraction postulate

Opposite sides of a parallelogram are congruent

P = sum of sides

Substitution postulate

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26

𝐶𝐷=26 Opposite sides of a parallelogram are congruent

𝐸𝐶=12𝐴𝐶 Diagonals of a parallelogram bisect each

other

26

7Substitution Postulate

𝐷𝐸=12𝐵𝐷 Diagonals of a parallelogram bisect each

other

𝐷𝐸=12

(28 )=14 Substitution Postulate

17

17 14

14

𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐶𝐸𝐷=17+14+26𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 ∆𝐶𝐸𝐷=57

P = sum of sides

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is the segment created by joining the midpoints of any two sides of a triangle

Page 45Mid-segment consruction

and

𝑋𝑌 ∥𝐵𝐶

VV

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𝑥=12

(30 )

𝑥=159

10

15

𝑝∆ 𝐴𝐵𝐶=++¿

𝑝∆ 𝐴𝐵𝐶=68

18

20

30

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𝒙=𝟓𝟎 (𝒄𝒐𝒓𝒓𝒆𝒔𝒑𝒐𝒏𝒅𝒊𝒏𝒈𝒂𝒏𝒈𝒍𝒆𝒔)

𝒚+𝟏𝟏𝟎=𝟏𝟖𝟎−𝟏𝟏𝟎−𝟏𝟏𝟎

𝒚=𝟕𝟎

∡𝑯𝑰𝑩=𝟒𝟎°∡𝑮𝑰𝑪=𝟔𝟏°

𝟒𝟎°𝟔𝟏°

𝒙+𝟏𝟎𝟏=𝟏𝟖𝟎−𝟏𝟎𝟏−𝟏𝟎𝟏

𝒙=𝟕𝟗

Homework – Page 48

A midpoint divides a segment into two congruent parts

Page 47

II

II

II

GIII III

Vertical angles are congruent

𝑆𝐴𝑆 ≅ 𝑆𝐴𝑆

Page 47

Corresponding parts of congruent triangles are congruent

I

When two lines are cut by a transversal so alt. int are lines are parallel

Partition postulate

Substitution

Division postulate