Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary...
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Transcript of Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary...
![Page 1: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Theorem 7.5: Triangle Proportionality Theorem Example 1: Find.](https://reader036.fdocuments.in/reader036/viewer/2022062713/56649f3e5503460f94c5e0ed/html5/thumbnails/1.jpg)
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Five-Minute Check (over Lesson 7–3)
CCSS
Then/Now
New Vocabulary
Theorem 7.5: Triangle Proportionality Theorem
Example 1: Find the Length of a Side
Theorem 7.6: Converse of Triangle Proportionality Theorem
Example 2: Determine if Lines are Parallel
Theorem 7.7: Triangle Midsegment Theorem
Example 3: Use the Triangle Midsegment Theorem
Corollary 7.1: Proportional Parts of Parallel Lines
Example 4: Real-World Example: Use Proportional Segments of Transversals
Corollary 7.2: Congruent Parts of Parallel Lines
Example 5: Real-World Example: Use Congruent Segments of Transversals
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Over Lesson 7–3
A. yes, SSS Similarity
B. yes, ASA Similarity
C. yes, AA Similarity
D. No, sides are not proportional.
Determine whether the triangles are similar. Justify your answer.
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Over Lesson 7–3
A. yes, AA Similarity
B. yes, SSS Similarity
C. yes, SAS Similarity
D. No, sides are not proportional.
Determine whether the triangles are similar. Justify your answer.
![Page 5: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Theorem 7.5: Triangle Proportionality Theorem Example 1: Find.](https://reader036.fdocuments.in/reader036/viewer/2022062713/56649f3e5503460f94c5e0ed/html5/thumbnails/5.jpg)
Over Lesson 7–3
A. yes, AA Similarity
B. yes, SSS Similarity
C. yes, SAS Similarity
D. No, angles are not equal.
Determine whether the triangles are similar. Justify your answer.
![Page 6: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Theorem 7.5: Triangle Proportionality Theorem Example 1: Find.](https://reader036.fdocuments.in/reader036/viewer/2022062713/56649f3e5503460f94c5e0ed/html5/thumbnails/6.jpg)
Over Lesson 7–3
A. 30 m
B. 28 m
C. 24 m
D. 22.4 m
Find the width of the river in the diagram.
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Content Standards
G.SRT.4 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
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You used proportions to solve problems between similar triangles.
• Use proportional parts within triangles.
• Use proportional parts with parallel lines.
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• midsegment of a triangle
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Find the Length of a Side
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Find the Length of a Side
Substitute the known measures.
Cross Products Property
Multiply.
Divide each side by 8.
Simplify.
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A. 2.29
B. 4.125
C. 12
D. 15.75
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Determine if Lines are Parallel
In order to show that we must show that
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Determine if Lines are Parallel
Since the sides are
proportional.
Answer: Since the segments have
proportional lengths, GH || FE.
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A. yes
B. no
C. cannot be determined
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Use the Triangle Midsegment Theorem
A. In the figure, DE and EF are midsegments of ΔABC. Find AB.
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Use the Triangle Midsegment Theorem
Answer: AB = 10
ED = AB Triangle Midsegment Theorem__12
5 = AB Substitution__12
10 = AB Multiply each side by 2.
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Use the Triangle Midsegment Theorem
B. In the figure, DE and EF are midsegments of ΔABC. Find FE.
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Use the Triangle Midsegment Theorem
Answer: FE = 9
FE = (18) Substitution__12
__12FE = BC Triangle Midsegment Theorem
FE = 9 Simplify.
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Use the Triangle Midsegment Theorem
C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE.
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Use the Triangle Midsegment Theorem
Answer: mAFE = 87
AFE FED Alternate Interior Angles Theorem
mAFE = mFED Definition of congruence
mAFE = 87 Substitution
By the Triangle Midsegment Theorem, AB || ED.
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A. 8
B. 15
C. 16
D. 30
A. In the figure, DE and DF are midsegments of ΔABC. Find BC.
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B. In the figure, DE and DF are midsegments of ΔABC. Find DE.
A. 7.5
B. 8
C. 15
D. 16
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C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD.
A. 48
B. 58
C. 110
D. 122
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Use Proportional Segments of Transversals
MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.
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Use Proportional Segments of Transversals
Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.
Answer: x = 32
Triangle Proportionality Theorem
Cross Products Property
Multiply.
Divide each side by 13.
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A. 4
B. 5
C. 6
D. 7
In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x.
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Use Congruent Segments of Transversals
ALGEBRA Find x and y.
To find x:
3x – 7 = x + 5 Given
2x – 7 = 5 Subtract x from each side.
2x = 12 Add 7 to each side.
x = 6 Divide each side by 2.
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Use Congruent Segments of Transversals
To find y:
The segments with lengths 9y – 2 and 6y + 4 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal.
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Use Congruent Segments of Transversals
Answer: x = 6; y = 2
9y – 2 = 6y + 4 Definition of congruence
3y – 2 = 4 Subtract 6y from each side.
3y = 6 Add 2 to each side.
y = 2 Divide each side by 3.
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Find a and b.
A. ;
B. 1; 2
C. 11;
D. 7; 3
__23
__32
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