Straight Lines Joining the Extremities of the Base of an Isosceles TriangleYour Headline
Here we will show that the straight lines joining the extremities of the base of an isosceles triangle to the midpoints of the opposite sides are equal.
Solution:
Given: In ∆XYZ, XY = XZ, M and N are the midpoints of XY and XZ respectively.
To prove: ZN = YM.
Proof:
|
Statement 1. XY = XZ 2. NY = \(\frac{1}{2}\)XY. 3. MZ = \(\frac{1}{2}\)XZ. 4. NY = MZ. 5. In ∆NYZ and ∆MYZ, (i) NY = MZ. (ii) YZ = YZ. (iii) ∠XYZ = ∠XZY. 6. ∆NYZ ≅ ∆MYZ. 7. ZN = YM. (Proved) |
Reason 1. Given. 2. N is the midpoint of XY. 3. M is the midpoint of XZ. 4. from statements 1, 2 and 3. 5. (i) From 4. (ii) Common side. (iii) XY = XZ. 6. By SAS criterion. 7. CPCTC. |
From Lines Joining the Extremities of the Base of an Isosceles Triangle 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.
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.