T Madas Two triangles are congruent if All

© T Madas

Two triangles are congruent if… All 3 sides are equal SSS 2 sides and the contained angle are equal SAS 1 side and the 2 adjacent angles are equal ASA © T Madas

© T Madas

Prove that the any point that lies on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment C Let AB be a line segment and M its midpoint Let C be a point on the perpendicular bisector Two right angled triangles are formed AM = MB A M B MC is common RAMC = RCMB = 90° The two triangles have two sides and the contained angle of those sides, correspondingly equal (SAS) Therefore the triangles are congruent AC = CB © T Madas

© T Madas

Given that a parallelogram has four equal sides, prove that its diagonals are perpendicular to each other. A parallelogram with 4 equal sides is in general a rhombus C D A RBDC = RABD as alternate angles B © T Madas

Given that a parallelogram has four equal sides, prove that its diagonals are perpendicular to each other. A parallelogram with 4 equal sides is in general a rhombus C D RBDC = RABD as alternate angles RDCA = RCAB as alternate angles A B © T Madas

Given that a parallelogram has four equal sides, prove that its diagonals are perpendicular to each other. A parallelogram with 4 equal sides is in general a rhombus C D RBDC = RABD as alternate angles RDCA = RCAB as alternate angles 0 r. DCA = r. CAB A S A hence all their sides are equal A B but all four sides of a rhombus are equal thus all four triangles are congruent S So RAOD = RDOC = RCOB = RAOB Since all four add up to 360°, each must be 90° © T Madas

© T Madas

In the diagram below ABCD and DEFG are squares. Prove that the triangles ADE and CDG are congruent. F E G A B D C © T Madas

In the diagram below ABCD and DEFG are squares. Prove that the triangles ADE and CDG are congruent. F E G A D = B + C © T Madas

In the diagram below ABCD and DEFG are squares. Prove that the triangles ADE and CDG are congruent. F E G A B D = + C © T Madas

In the diagram below ABCD and DEFG are squares. Prove that the triangles ADE and CDG are congruent. F E SAS G A D ADE and CDG are congruent because 2 sides and the contained angle of ADE are equal to 2 sides and the contained angle of ADE. B C © T Madas

© T Madas

In a circle, centre O, two chords AB and CD are marked, so that AB = CD Prove that the chords are equidistant from the centre O B Need to prove OM = ON If we prove that AOB and COD are congruent then their corresponding heights OM and ON will be equal M O A C N D AB = CD (given) AO = CO (circle radii) BO = DO (circle radii) Triangle congruency SSS OM = ON © T Madas

© T Madas

In the diagram below ABD and BCE are equilateral triangles. Prove that the triangles ABE and DBC are congruent. D A 60° θ B 60° AB = DB BC = BE RDBC = RABE [ABD is equilateral] [CBE is equilateral] [both angles are 60° + θ ] VABE and VDBC are congruent because 2 sides and the contained angle of VABE are equal to 2 sides and the contained angle of VDBC. SAS C E © T Madas

© T Madas