In triangle ABC, let M be the midpoint of AB and N be the midpoint of AC. Suppose that you measure MN and find it to be 7.3 cm long. How If you were to measure angles AMN and ABC, what would you find? long would BC be?
In triangle ABC, let M be the midpoint of AB and N be the midpoint of AC. Suppose that you measure MN and find it to be 7.3 cm long. How If you were to measure angles AMN and ABC, what would you find? long would BC be?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please answer the question in the picture. Answer all parts, thank you
![**Triangle Midsegment Theorem**
In triangle ABC, let \( M \) be the midpoint of \( AB \) and \( N \) be the midpoint of \( AC \).
Suppose that you measure \( MN \) and find it to be 7.3 cm long. How long would \( BC \) be?
If you were to measure angles \( AMN \) and \( ABC \), what would you find?
**Explanation of the Theorem:**
- According to the Triangle Midsegment Theorem:
- \( MN \) is parallel to \( BC \).
- \( MN \) is half the length of \( BC \).
**Given Data:**
- \( MN = 7.3 \) cm
**Calculation:**
- Since \( MN \) is parallel to \( BC \) and half its length:
\[ BC = 2 \times MN = 2 \times 7.3\, \text{cm} = 14.6\, \text{cm} \]
Therefore, \( BC \) would be 14.6 cm long.
**Angles:**
- \( \angle AMN = \angle ABC \), because \( MN \parallel BC \). This means the angles are congruent due to the Corresponding Angles Postulate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F936aff3a-ee4b-4b26-80f0-88e824df4b12%2Fc336c08b-4507-4b5e-abe9-dc134474095b%2F6m0hoin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Triangle Midsegment Theorem**
In triangle ABC, let \( M \) be the midpoint of \( AB \) and \( N \) be the midpoint of \( AC \).
Suppose that you measure \( MN \) and find it to be 7.3 cm long. How long would \( BC \) be?
If you were to measure angles \( AMN \) and \( ABC \), what would you find?
**Explanation of the Theorem:**
- According to the Triangle Midsegment Theorem:
- \( MN \) is parallel to \( BC \).
- \( MN \) is half the length of \( BC \).
**Given Data:**
- \( MN = 7.3 \) cm
**Calculation:**
- Since \( MN \) is parallel to \( BC \) and half its length:
\[ BC = 2 \times MN = 2 \times 7.3\, \text{cm} = 14.6\, \text{cm} \]
Therefore, \( BC \) would be 14.6 cm long.
**Angles:**
- \( \angle AMN = \angle ABC \), because \( MN \parallel BC \). This means the angles are congruent due to the Corresponding Angles Postulate.
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