down votefavorite1I am supposed to use the following 8 theorems only to prove the above prepositions:Theorem 1: If a ray stands on a line , then the sum of the adjacent angles formed is 180deg.Theorem 2: If two lines intersect , then the vertically opposite angles are equal.Theorem 3: If a transversal cuts two parallel lines, then each pair of alternate angles are equal, and the interior angles on the same side of the transversal are supplementary.Theorem 4: Lines which are parallel to the same line are parallel to each other.Theorem 5: The sum of the three angles of a triangle is 180deg.Theorem 6: If one side of a triangle is produced , the exterior angle so formed is equal to the sum of the interior opposite angles.Theorem 7: The angles opposite to equal sides of a triangle are equal in an isosceles triangle.Theorem 8: The bisector of the vertical angle of an isosceles triangle bisects the base and is perpendicular to the base.
Step 1 : Construct a right angled triangle (name it ABC) . Let AB be the hypotenuse side . Angle C be 90 
Step 2 : From C as center cut 2 arcs on line segment AB. Mark the 2 meeting points as X and Y.
Step 3 : From X as center , measuring 3/4 length of XY draw 2 arcs on both the sides of the line .
Step 4 : From Y as center , with the same measurement draw 2 arcs on both the sides of the line  such that it meets the arc drawn from X. Name one meeting point as M and another as N.
Step 5 : From C  draw a line such that it passes through M and N .
This line would be the perpendicular from the right angle of the triangle to the hypotenous .