Congruent Triangles

Part IIClass VII

CONGRUENCE CONDITIONS

IF THREE SIDES AND THREE ANGLES OF

ONE ARE EQUAL TO THREE SIDES AND

THREE ANGLES OF ANOTHER

(total six sets)

A TRIANGLE

IS CONGRUENT TO

ANOTHER TRIANGLE

BUT WITH ONLY THREE SETS OF EQUALITIES ( INSTEAD OF SIX SETS OF EQUALITIES) THE TWO TRIANGLES WILL PROVED TO BE CONGRUENT. THAT IS THE OTHER THREE SETS ARE FOUND TO BE EQUAL AUTOMATICALLY.

CONGRUENCE CONDITIONS

THE THREE SETS OF EQUALITIES ARE

*SSS ( THREE SIDES OF TWO s )

*ASA ( TWO ANGLES AND THE

INCLUDED SIDE OF TWO s )

*SAS (TWO SIDES AND THE INCLUDED

ANGLE OF TWO s )

*RHS ( HYPOTENUSE, A SIDE OF TWO

RIGHT ANGLED s )

CONGRUENCE CONDITIONS

SSSSSS

SASSAS

ASAASA

RHSRHSLET US LEARN ABOUT

THIS HERE

SSS CONGRUENCE CONDITION

Two Triangles are

congruent if

THREE sides

of one triangle are respectively equal to the

THREE sides

of the other triangle

SSS CONGRUENCE CONDITION

ONE SET OF EQUAL SIDES

ANOTHER SET OF EQUAL SIDES

THIRD SET OF EQUAL SIDES

FORM CONGRUENT TRIANGLES

Side –Angle – Side (SAS) Congruence Condition

Two Triangles are congruent if two sides and the included angle of one triangle are respectively equal to the two sides and the included angle of the other triangle

Side –Angle – Side (SAS) Condition

12

S

A

S

INCLUDED ANGLES

FOR SIDE (GREEN) & SIDE (PINK)

“ 1 ” IS THE INCLUDED ANGLE.

12

FOR SIDE (PINK) &SIDE (YELLOW) “ 2 ” IS THE INCLUDED ANGLE

FOR THE GIVEN PAIR OF SIDES FIND THE INCLUDED

ANGLE

P Q

RS

1. Sides PR & PQ

2. Sides RS &PS

3. Sides PQ & PS

4. Sides RS & RQ

5. Sides SO &PO

O

Write the answers in the note book, click next slide for checking.

CHECK THE ANSWERS

1. RPQ

2. PSR

3. SPQ

4. SRQ

5. SOP

REMEMBERIN ‘SAS’ CONDITION THE

ANGLE MUST BE AN INCLUDED ANGLE .

THE TRIANGLES NEED NOT BE CONGRUENT IF THE ANGLES ARE NOT “INCLUDED”

Side –Angle – Side (SAS) Condition

1

A SIDE (PINK)

Another side

(GREEN)

One Angle but not includedONE

With the same measurement ,Another

THEY ARE NOT CONGRUENT!!!

RHS CONGRUENT CONDITION

R Right angle

H hypotenuse

S any side other than

hypotenuse

Two RIGHT Triangles are congruent if HYPOTENUSE & ONE SIDE of one triangle are

respectively equal to the HYPOTENUSE & ONE SIDE of the other RIGHT Triangle

RHS CONGRUENCE CONDITION