5.3 Congruent Angles Associated With Parallel Lines By: Kristi Polizzano.
Page 43 Statements Reasons 1. Given 2. Corresponding parts of congruent figures are congruent 3....
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Page 43
Statements
Reasons
๐๐๐ข๐๐๐ ๐ด๐ต๐ถ๐โ ๐๐๐ข๐๐๐๐ธ๐น๐บ๐1. 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
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UNIT 3Lesson 10 โ Mid-segment of a
Triangle
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Page 43
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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๐+4=15โ4โ4๐=11
๐ถ๐ท=15๐ด๐ท=3 (11)+2=35๐ถ๐ต=35
๐๐๐๐๐๐๐ก๐๐=15+15+35+35๐๐๐๐๐๐๐ก๐๐=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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Page 44
26
๐ถ๐ท=26 Opposite sides of a parallelogram are congruent
๐ธ๐ถ=12๐ด๐ถ Diagonals of a parallelogram bisect each
other
26
7Substitution Postulate
๐ท๐ธ=12๐ต๐ท Diagonals of a parallelogram bisect each
other
๐ท๐ธ=12
(28 )=14 Substitution Postulate
17
17 14
14
๐๐๐๐๐๐๐ก๐๐ ๐๐ โ๐ถ๐ธ๐ท=17+14+26๐๐๐๐๐๐๐ก๐๐ ๐๐ โ๐ถ๐ธ๐ท=57
P = sum of sides
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is the segment created by joining the midpoints of any two sides of a triangle
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Page 45Mid-segment consruction
and
๐๐ โฅ๐ต๐ถ
VV
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Page 46
๐ฅ=12
(30 )
๐ฅ=159
10
15
๐โ ๐ด๐ต๐ถ=++ยฟ
๐โ ๐ด๐ต๐ถ=68
18
20
30
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๐=๐๐ (๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐)
๐+๐๐๐=๐๐๐โ๐๐๐โ๐๐๐
๐=๐๐
โก๐ฏ๐ฐ๐ฉ=๐๐ยฐโก๐ฎ๐ฐ๐ช=๐๐ยฐ
๐๐ยฐ๐๐ยฐ
๐+๐๐๐=๐๐๐โ๐๐๐โ๐๐๐
๐=๐๐
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Homework โ Page 48
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A midpoint divides a segment into two congruent parts
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II
II
II
GIII III
Vertical angles are congruent
๐๐ด๐ โ ๐๐ด๐
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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