Post on 19-Dec-2015
transcript
© 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
Prove that the any point that lies on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment
A BM
C Let AB be a line segment and M its midpointLet C be a point on the perpendicular bisectorTwo right angled triangles are formedAM = MB MC is commonAMC = CMB = 90°
The two triangles have two sides and the contained angle of those sides, correspondingly equal (SAS)Therefore the triangles are congruentAC = CB
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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 arhombus
A B
CDBDC = ABD
as alternate angles
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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 arhombus
A B
CDBDC = ABD
as alternate angles
DCA = CABas alternate angles
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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 arhombus
A B
CDBDC = ABD
as alternate angles
DCA = CABas alternate angles
DCA = CAB0
A S A
hence all their sides are equal
but all four sides of a rhombus are equal
thus all four triangles are congruent
So AOD = DOC = COB = AOB
Since all four add up to 360°, each must
be 90°
S S S
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A
B C
D
E
F
G
In the diagram below ABCD and DEFG are squares.Prove that the triangles ADE and CDG are congruent.
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A
B C
D
E
F
G
AD = DC
GD = DE
= +
In the diagram below ABCD and DEFG are squares.Prove that the triangles ADE and CDG are congruent.
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A
B C
D
E
F
G
AD = DC
GD = DE
= +
= +
GDC =R GDAR 90+ °
ADE =R GDAR 90+ °
GDC =R ADER
In the diagram below ABCD and DEFG are squares.Prove that the triangles ADE and CDG are congruent.
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A
B C
D
E
F
G
AD = DC
GD = DE
GDC =R ADERSAS
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.
In the diagram below ABCD and DEFG are squares.Prove that the triangles ADE and CDG are congruent.
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A
B
C D
O
In a circle, centre O, two chords AB and CD are marked, so that AB = CDProve that the chords are equidistant from the centre O
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
N
(given)(circle radii)(circle radii)
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In the diagram below ABD and BCE are equilateral triangles.Prove that the triangles ABE and DBC are congruent.
A
B
C
D
E
AB = DB [ABD is equilateral]
BC = BE [CBE is equilateral]
θ
60°
60°
DBC = ABE [both angles are 60° + θ ]
SAS
ABE and DBC are congruent because 2 sides and the contained angle of ABE are equal to 2 sides and the contained angle of DBC.