Explanation Given information: To show that the line segment joining the midpoints of any two sides of a given triangle is parallel to the third side and has half its length Calculation: This is the Midpoint theorem statement.The proof of the theorem is as follows, Consider a triangle ABC. Let P and Q be the mid-points of sides AB and AC respectively In Δ A P Q and Δ C R Q , the angles are vertically opposite, ∠ A Q P = ∠ C Q R (Vertically opposite) P Q = Q R (by construction) The midpoints is given by, A Q = C Q (Q is the mid-point of AC) ∴ Δ A P Q ≅ Δ C R Q (SAS congruence criterion) ⇒ A P = C R (By C.P.C.T) … (1) And ∠ A P Q = ∠ C R Q (By C.P.C.T) … (2) It is given that P is the mid-point of AB ∴ A P = P B … (3) From (1) and (3) P B = C R … ( 4 )

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 1, Problem 73SP

To determine

To prove that the line segment joining the midpoints of any two sides of

a given triangle is parallel to the third side and has half its length.

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Chapter 1, Problem 72SP

Chapter 1, Problem 74SP

Chapter 1 Solutions

Calculus

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To prove that the line segment joining the midpoints of any two sides of a given triangle is parallel to the third side and has half its length.

Solution Summary: The author explains the Midpoint theorem, where P and Q are the mid-points of sides AB and AC.

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To prove that the line segment joining the midpoints of any two sides of a given triangle is parallel to the third side and has half its length.

Want to see the full answer?

Chapter 1 Solutions

To prove that the line segment joining the midpoints of any two sides of

a given triangle is parallel to the third side and has half its length.