Math Problem Statement

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ΔABC is an isosceles triangle with A⁢B―=B⁢C―=6 units. D and E are the midpoints of A⁢B― and B⁢C―, respectively.

 The length of A⁢C― is 8 units. The length of D⁢E― is  units.

Solution

To find the length of segment DEDE, we can use the midsegment theorem for triangles. This theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

In this case, DEDE is the midsegment connecting the midpoints of ABAB and BCBC, so:

DE=12×ACDE = \frac{1}{2} \times AC

Given that AC=8AC = 8 units, the length of DEDE is:

DE=12×8=4 unitsDE = \frac{1}{2} \times 8 = 4 \text{ units}

The length of DEDE is 4 units.

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:

  1. What are the properties of midsegments in different types of triangles?
  2. How does the midsegment theorem apply to right triangles?
  3. Can you find the perimeter of the triangle using the given information?
  4. What is the area of triangle ABCABC?
  5. How do the medians and midsegments of a triangle differ?

Tip: Midsegments divide triangles into smaller, similar triangles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Midsegments

Formulas

DE = 1/2 * AC

Theorems

Midsegment Theorem

Suitable Grade Level

Grades 8-10