Proof By the Equal Intercepts Theorem

Here we will prove that in the given XYZ, M and N are the midpoints of XY and XZ respectively. T is any point on the base YZ. Prove that MN bisects XT.

Proof By the Equal Intercepts Theorem

Solution:

Given: In ∆XYZ, XM = MY and XN = NZ. MN cuts XT at U.

To prove: XU = UT.

Construction: Through X, draw PQ ∥ YZ.

Proof:

            Statement

            Reason

1. MN ∥ YZ.

1. The line segment joining the midpoints of the two sides of a triangle is parallel to the third side.

2. PQ ∥ MN ∥ YZ.

2. PQ ∥ YZ and MN ∥ YZ.

3. The transversal XY makes equal intercepts on PQ, MN and YZ.

3. Given that XM = MY.

4. The transversal XT also makes equal intercepts on PQ, MN and YZ.

4. By the Equal Intercepts Theorem.

5. XU = UT. (Proved)

5. From statement 4.




9th Grade Math

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