1. Congruence Human Products : God’s creation:
Congruence are objects that have same shape and same size

2. Similarity Human Product : God’s creation :
Similar objects have same shape but different size , their corresponding length has same ratio

3. Previous Congruence & Similarity Review
Which pairs are congruence & similar ? K J L
20o G A 12 B C
20o D E F 3 9 H I 5
KLM = DEF = 70o
AC/GH = 9/3 = 3
AC/GH = BC/ HI
= BC / BC = 15
AC/GH = AB/GI
= 12/GI GI = 12/3 = 4
KLM = ?
Ratio of similarity?
Length of BC?
Length of GI?

4. SSS Proofs / reasons of PQR & PRS congruent with type SSS :
Investigation
Using ice cream sticks, construct triangles with side 5, 8 , 10 cm and 10 , 5 , 8 cm Connect them with glue/ cellotape . Mark each edge of them with letter ABC & DEF . Then compare the shape by measure their angles and size. What is your conclusion ?
Practice Now 1 P Q S E D 10 8 5 F A 10 B C 5 8 R R
Proofs / reasons of PQR & PRS congruent with type SSS :
Side QR = RS (given)
Side PQ = PS (given)
Side PR = PR (overlap)
This type is called SSS (Side Side Side)

5. SAS
Investigation : Draw triangles ABC with side AB = 6cm and AC = 3 cm with angle between them is 50o. Draw another with AB = 3 cm and AC = 6 cm with angle between them is 50o. Measure all sides and angles in both triangles. What is your conclusion ? X Y Z
50o
XYZ and ABC are called included angles ; angle between corresponding sides. They are called congruent with type SAS (Side Angle Side) A B C D E
Proofs / reasons of ABC & CDE congruent type SAS :
Side AC = CD (given)
Angle ACB = ECD (opposite)
Side BC = CE (given)
Worked Examples 2
page 298
Practice Now 2 page 298

6. SSA Draw picture ABC of page 297
Draw another XYZ which 3 cm side goes inward (move inside)
Measure all sides of them and compare.
What is your conclusion between them ? A B C Y X Z
30o
Practice Now 3 page 299
They are different in last sides and 2 angles.
so the SSA is not congruent.

7. ASA or AAS Proofs of DEF & EFG congruent ASA :
Worked Examples 4
page 301
Practice Now 4 page 302
Investigation :
Draw triangle at page 300
Draw another triangle but 60o at left and 40o at right and 7 cm in the middle
Measure all angles and sides of them.
Compare them, what is your conclusion ? R P Q A C B
40o
60o C A B Z Y X
50o
70o
Side between 2 angles or 2 angles known & 1 side known are congruent triangles
ASA Type & AAS Type are the same.
60o
60o D E F G H
Proofs of DEF & EFG congruent ASA :
Angle EDF = FGH (alternate angles)
Side DE = GH (given)
Angle DEF= FGH (alternate angles)

8. Type RHS 5 13 5 Worked Examples 5 13 page 303 Practice Now 5 page 303
Proof :
DE = KL (Side given)
DF = JL (Hypotenuse given)
DEF =  JKL (right angled given) K J L D E F 13 5
Worked Examples 5
page 303
Practice Now 5 page 303 13
The above type is one of type of congruence : RHS (Right angle Hypotenuse Side)
DE2 + EF2 = DF2 so 52 + EF2 = EF = (169 – 25) =  144 = 12
JK2 + KL2 = JL so JK = JK = (169 – 25) =  144 = 12
So the right angled triangle with 1 side & 1 hypotenuse side, and right angle known is congruent.

9. Types of Congruence Congruent : SSS SAS ASA or AAS RHS Not Congruent :
AAA
Class Discussion page 304
Exercise 9A page 305

10. Similarity Recap
- All corresponding angles is the same : BAC = YXZ ,  ABC = XYZ ,  ACB =  XZY - Ratio of corresponding sides is the same : AB / XY = BC / YZ = AC / XZ = constant = k X Y Z A B C 5 10 ? 14

11. Test of Similarity
The test is like congruent , the difference is the length is not marked.
AA or AAA
SSS
SAS C A B C A B
30o
50o
Examples 6, 7, 8, 9
Page
Practice Now 6, 7, 8, 9
30o
50o E 2 D F 3 4 Q 4 P R 6 8 E 3 D F 5 Q
4.5 P R
7.5
70o
70o

12. Various Forms of SimilarityB C D E F G H D A B C E A B C D E A B C D E C A B D A B C D F A B E D C G E F