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.
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. |
From Proof By the Equal Intercepts Theorem to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jul 12, 24 03:08 PM
Jul 12, 24 02:11 PM
Jul 12, 24 03:21 AM
Jul 12, 24 12:59 AM
Jul 12, 24 12:30 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.