Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Continuing Congruence

No description
by

Mr Mattock

on 12 December 2017

Comments (0)

Please log in to add your comment.

Report abuse

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
Answers

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
Full transcript