A student constructed a triangle with the known conditions to him bein

1.	A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to ∠B and angle MYX equal to ∠C 3. Bisect ∠LXY and ∠MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors DE of AX and FG of AY 5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?
Answer» A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to $∠ B$ and angle MYX equal to $∠ C$ 3. Bisect $∠ L X Y$ and $∠ M X Y$ . Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors DE of AX and FG of AY 5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to ∠B and angle MYX equal to ∠C 3. Bisect ∠LXY and ∠MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors DE of AX and FG of AY 5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?

Answer»

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows:

1. Draw a line segment, say XY equal to AB + BC + AC

2. Make angles LXY equal to $∠ B$ and angle MYX equal to $∠ C$

3. Bisect $∠ L X Y$ and $∠ M X Y$ . Let these bisectors intersect each other at A.

4. Draw perpendicular bisectors DE of AX and FG of AY

5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC.

6. The triangle ABC is thus formed.

How many isosceles triangles are there in this figure?

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