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# Continuing Congruence

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by

## Mr Mattock

on 12 December 2017

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#### Transcript of Continuing Congruence

Continuing Congruence
Starter
L.O. - To understand the minimum requirements to make a triangle unique, and prove two triangles are congruent using these requirements.
Proving Congruence
Main Activity
Complete the congruence sheet.
Main Activity
Complete the congruence sheet.
(i) Yes - SSS (ii) Yes - ASA
(iii) Yes - RHS (iv) Yes - ASA
(v) No (vi) No

2) i) Yes - SAS
ii) No
iii) Yes - RHS
iv) Yes - RHS
v) No
Main Activity
3). YZ is common to both.
Angle XYZ = Angle XZY (Isosceles triangle angles)
Angle MYZ = Angle NZY (Given in question)
So by ASA triangle YMZ is congruent to ZNY.

4). AB = DC
Angle BDC = DBA (alternate angles in parallel lines)
Angle ACD = CAB (alternate angles in parallel lines)
So by ASA triangle ABE and CDE are congruent
Key
Examples

Activities
Activity

Worked
Example

PRS and RQT are both equilateral triangles.

Write down as many sides and angles that are the same as you can. Give reasons why they are the same.
Starter
PS = SR = RT = TQ = SR.

SPR = PSR = SRP = SRT = TRQ = RTQ = TQR.

SPT = RPT = RQS = TQS
(a) Prove that
PSQ is congruent to QTP.

(b) Hence prove that PUS = QUT
U
Proving Congruence
(a) Prove that
PSQ is congruent to QTP.

(b) Hence prove that PUS = QUT
U
(a) PQ is part of both triangles. PS = QT (equilateral triangles).
SPR = TQR (equilateral triangles). So by SAS, PSQ = QTP
(b) PS = QT (equilateral triangles). PT = QS (because of result (a)) and so PU = QU. Angle PSU = QTU = 90 degrees. So by RHS, PUS = QUT.
Plenary
Draw the three possible triangles with these properties:

One side of 7 cm, one side of 9 cm, one angle of 30 .
o
Plenary
Draw the three possible triangles with these properties:

One side of 7 cm, one side of 9 cm, one angle of 50 .
o
7 cm
9 cm
50
o
7 cm
9 cm
50
o
7 cm
9 cm
50
o
U
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