Q32. Draw an isosceles triangle and t... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q32. (page 139)

Draw an isosceles triangle and then join the midpoints of its sides to form another triangle. What can you deduce about this second triangle? Explain.

Short Answer

Expert verified

The second triangle is also an isosceles triangle.

Step by step solution

– Draw a diagram.

A figure shows $螖 A B C$ is an isosceles triangle with $\overset{炉}{A B} 鈮� \overset{炉}{A C}$ and $D, E, F$ are the mid points of sides, $A B, A C$ and $B C$ respectively.

By joining the midpoints of sides of $螖 A B C$ another $螖 D E F$ is formed.

– Description of step.

A line segment which joins the midpoints of two sides of the triangle has a length equal to half the length of the third side.

Therefore, from the figure we can conclude that

$\begin{matrix} \overset{炉}{D E} = \frac{1}{2} \overset{炉}{B C} \\ \overset{炉}{E F} = \frac{1}{2} \overset{炉}{A B} \\ \overset{炉}{D F} = \frac{1}{2} \overset{炉}{A C} \end{matrix}$

– Description of step.

As $螖 A B C$ is an isosceles triangle, $\overset{炉}{A B} = \overset{炉}{A C}$ . Multiply both the sides of $\overset{炉}{A B} = \overset{炉}{A C}$ by $\frac{1}{2}$ .

$\begin{matrix} \frac{1}{2} \overset{炉}{A B} = \frac{1}{2} \overset{炉}{A C} \\ \overset{炉}{E F} = \overset{炉}{D F} \end{matrix}$

Therefore, by definition of an isosceles triangle, $螖 D E F$ is also an isosceles triangle with $\overset{炉}{E F} 鈮� \overset{炉}{D F}$ .

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91影视

Draw an isosceles triangle and then join the midpoints of its sides to form another triangle. What can you deduce about this second triangle? Explain.

Short Answer

Step by step solution

– Draw a diagram.

– Description of step.

– Description of step.

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