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1.06 Intro to Proofs

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Adjacent angles --> share a side

The presence of a segment bisector will result in congruent segments.

Vertical angles --> angles directly across from eachother

Definition of midpoint --> The point of a line segment that divides it into two parts of the same length.

If T is the midpoint of line RS then, line RT is congruent to line TS

Complementary angles --> must add up to 90°

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Distributive property: 4(x +5) = 2x + 2 --> 4(x) + 4(5) => 4x + 20 = 2x +2

Sub. Prop. of Equality: 4x + 20 = 2x + 2 --> (4x -2x) + 20 = 2 => 2x + 20 = 2

Sub. Prop. of Equality: 2x + 20 = 2 --> 2x = (2 -20) => 2x = -18

Div. Prop of Equality: 2x = -18 --> (2x/2) = (-18/2) => x = -9

If LR = 12 and LP = 7, find PR. Explain

PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution

alternatively: 7 + x = 12 --> 12 - 7 = 5 --> x = 5 --> PR = 5 :]

If E is the midpoint of line AB and AB = 30, what is AE

Segment AE is half of line AB, and therefore the length is half of 30

Segment AE = 15

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If m

Using the Angle Addition Postulate , 40 + m

If ray JG is an angle bisector of

we know that ray JG is a bisector, so x = 30, and therefore

30 + 30 = 60°

If E is the midpoint of line AB and AB = 30, what is AE

Segment AE is half of line AB, and therefore the length is half of 30

Segment AE = 15

If LR = 12 and LP = 7, find PR. Explain

PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution

alternatively: 7 + x = 12 --> 12 - 7 = 5 --> x = 5 --> PR = 5 :]

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Distributive property: 4(x +5) = 2x + 2 --> 4(x) + 4(5) => 4x + 20 = 2x +2

Sub. Prop. of Equality: 4x + 20 = 2x + 2 --> (4x -2x) + 20 = 2 => 2x + 20 = 2

Sub. Prop. of Equality: 2x + 20 = 2 --> 2x = (2 -20) => 2x = -18

Div. Prop of Equality: 2x = -18 --> (2x/2) = (-18/2) => x = -9

If ray JG is an angle bisector of <FJH, find m<FJH

we know that ray JG is a bisector, so x = 30, and therefore

30 + 30 = 60°

If m

Using the Angle Addition Postulate , 40 + m

1.07 Line and Angle Proofs

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