SOLUTION: given: angle 1 is congruent to angle 2 prove: tiangle JOE is isosceles (please really need help.. i'm bad in geometry..)

Algebra ->  Geometry-proofs -> SOLUTION: given: angle 1 is congruent to angle 2 prove: tiangle JOE is isosceles (please really need help.. i'm bad in geometry..)      Log On


   

Question 255998: given:
angle 1 is congruent to angle 2
prove:
tiangle JOE is isosceles



(please really need help.. i'm bad in geometry..)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
triangle is JOE.

J is on top.
O is bottom left.
E is bottom right.

angle 1 is angle JOE.

that's the angle on the bottom left corner of the triangle.

angle 2 is angle JEO.

that's the angle on the bottom right corner of the triangle.

drop a perpendicular from J to intersect with the line OE at point L.

line JL is perpendicular to line OE at L.

this means that angle JLO is 90 degrees and angle JLE is also 90 degrees.

you have formed 2 right triangles.

they are triangle JLO and triangle JLE.

These triangles are congruent by AAS.

AAS means 2 corresponding angles and the non-included side.

The angles that are congruent are JOE and JEO and JLO and JLE.

The non-included sides that are congruent are JL and JL. Since this line is part of both triangles, then it is congruent to itself.

Since the triangles are congruent, then their corresponding sides are congruent.

This means that side JO is congruent to side JE.

Your original triangle is JOE.

JOE is an isosceles triangle because it has 2 sides that are congruent to each other.

proof is done.

triangle we used in this proof is shown below: 


                                     J
                                     x
                                   x x x
                                 x   x   x
                               x     x     x
                             x       x       x
                           x         x         x
                         x           x           x
                       x             x             x
                     x               x               x
                   x                 x                 x
                 x                   x                   x
               x    1           3    x   4            2    x
           O x x x x x x x x x x x x x x x x x x x x x x x x x E
                                     L

angle JOE is the same as angle 1.
angle JEO is the same as angle 2.
angle JLO is the same as angle 3.
angle JLE is the same as angle 4.

note that angle JOE is the same as angle JOL is the same as angle 1.
note that angle JEO is the same as angle JEL is the same as angle 2.