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SSS SAS ASA Two triangles are congruent if… All 3 sides are equal 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 MC is common RAMC = RCMB = 90° A B M 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 RBDC = RABD as alternate angles D C 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 RBDC = RABD as alternate angles D C RDCA = RCAB as alternate angles A B © T Madas

RBDC = RABD RDCA = RCAB rDCA = rCAB 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 RBDC = RABD as alternate angles D C RDCA = RCAB as alternate angles rDCA = rCAB 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 So RAOD = RDOC = RCOB = RAOB Since all four add up to 360°, each must be 90° S S S © T Madas

Exam Question © 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 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 D = + = + B C © T Madas

SAS In the diagram below ABCD and DEFG are squares. Prove that the triangles ADE and CDG are congruent. F SAS E 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

Exam Question © T Madas

Triangle congruency SSS OM = ON (given) (circle radii) 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 AB = CD AO = CO BO = DO Triangle congruency SSS OM = ON M O A (given) (circle radii) C D N © T Madas

© T Madas

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

© T Madas