LAVESH DHADIWAL &DHIRAJ PATIDARCLASS – 10TH

SUBJECT – MATHMATECISSUMMATIVE ASSESMENT – IIFORMATIVE ASSESMENT – IIIACTIVITY – V

PRESENTING BY

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TRIANGLES

CONTENTS•INTRODUCTION •CONGRUENT TRIANGLE• SIMILAR TRIANGLE • CONGRUENCY RULES • SIMILARITY RULES

INTRODUCTIONTRIANGLE IS A CLOSED FIGURE BOUNDED BY THREE LINE SEGMENTS .

IT HAS THREE VERTEX ,THREE ARMS (SIDES) AND THREE ANGLES .

A

CB

VERTEX

ANGLE

ARM(SIDE)

TRIANGLE

LINE SEGMENTS AB,BC,CA

SIDES AB,BC,CA

VERTEX A,B,C

ANGLE ⦟ABC , BCA , ⦟BAC⦟

CONCLUSION

TWO TRIANGLES ARE SAID TO BE CONGRUENT, WHEN ALL SIDES AND ALL ANGLES OF ONE ARE EQUAL TO CORRESPONDING SIDES

AND ANGLES OF THE OTHER.

CONGRUENCY OF TRIANGLES

TRIANGLES ‘ABC’ AND ‘PQR’ ARE SAID TO BE CONGRUENT IF SIDES AB,BC AND CA OF TRIANGLE ‘ABC’ ARE EQUAL TO SIDES PQ,QR

AND PR OF TRIANGLE PQR AND A⦟ , B ⦟ AND C ⦟ OF TRIANGLE ABC ARE EQUAL TO P⦟ , Q⦟ , R ⦟ OF TRIANGLE PQR RESPECTIVELY .

A

CB

P

RQ

IF △ ABC ≌ △PQRTHEN• AB=PQ• BC=QR • AC=PR • ⦟A= P ⦟• ⦟B= Q ⦟• ⦟C= R ⦟

CONCLUSION

SIMILARITY OF TRIANGLESTWO TRIANGLES ARE SAID TO BE SIMILAR, IF THEIR

CORRESPONDING ANGLES ARE EQUAL AND CORRESPONDING SIDES ARE PROPORTIONAL.

B

A

C

P

RQ

TRIANGLES ‘ABC’ AND ‘PQR’ ARE SAID TO BE SIMILAR IF A⦟ , B ⦟AND C ⦟ OF TRIANGLE ABC ARE EQUAL TO CORRESPONDING P⦟ , Q⦟ , R ⦟ OF TRIANGLE PQR AND SIDES AB, BC, AC OF TRIANGLE ABC ARE PROPORTIONAL TO CORRESPONDING SIDES PQ, QR AND PR OF TRIANGLE PQR .

IF △ABC∼ △PQR , THEN• ⦟A= P ⦟• ⦟B = Q ⦟• ⦟C= R⦟

• AB/PQ= BC/QR=AC/PR

CRITERIA OF CONGRUENCY OF TRIANGLES

• Side Angle Side (SAS) congruency rule. • Angle Side Angle (ASA) congruency rule. • Side Side Side (SSS) congruency rule. • Angle Angle Side (AAS) congruency rule. • Right Angle-Hypotenuse-Side (RHS) congruency rule. ≅

(SIGN OF CONGRUENCY)

Side Angle Side (SAS) congruence criterion

RQ

PA

CB

\\| |

△ ABC ≅ △ PQR SINCE , IN △ ABC and △ PQR AB = PQ (sides) BC = QR (sides) ⦟B = Q ⦟(angles)

Two triangles are congruent if two sides and included angle of one triangle are equal to corresponding two sides

and the included angle of the other triangle.

By SAS congruence criterion

Included angles refers to equal angle included between the sides.

A

CB RQ

P

\| |

\\\ \\

Side Side Side (SSS) congruency criterion

Two triangles are congruent if three sides of one triangle are equal to corresponding sides of the other triangle.

SINCE , IN △ ABC and △ PQR AB = PQ BC = QR AC = PRBy SSS congruency criterion△ ABC ≅ △ PQR

A

CB

P

RQ

| |

Angle Angle Side (AAS) congruency rule

Two triangles are congruent if two angles and any one side of one triangle are equal to two angles and corresponding

side of the other triangle.

SINCE , IN △ ABC and △ PQR ⦟B = Q⦟ AC = PR ⦟C = R⦟△ ABC ≅ △ PQR By AAS congruence criterion

A

CB

P

RQ| |

Angle Side Angle (ASA) congruency rule

Two triangles are congruent if two angles and included side of one triangle are equal to two angles and the

included side of the other triangle.

Included side refers to equal side included

between the angles.

SINCE , IN △ ABC and △ PQR ⦟B = Q⦟ BC = QR ⦟C = R⦟△ ABC ≅ △ PQR By ASA congruence criterion

P

RQB

A

C

\ \| |

Right Angle-Hypotenuse-Side (RHS) congruency rule

Two right angled triangles are congruent if one side and the hypotenuse of one triangle are equal to one side and the

hypotenuse of the other triangle.SINCE , IN △ ABC and △ PQR ⦟B = Q ( right angle)⦟ BC = QR (one side or base) AC = PR (hypotenuse)By RHS congruency criterion△ ABC ≅ △ PQR

CRITERIA OF SIMILARITY OF TRIANGLES

• Angle Angle Angle (AAA) similarity rule. • Side Side Side (SSS) similarity rule. • Angle Angle (AA) similarity rule. ∼(SIGN OF SIMILARITY)

A

CB

P

RQ

Angle Angle (AA) similarity rule

Two triangles are similar if two angles of one triangle are equal to corresponding angles of the other triangle.

SINCE, IN △ ABC and △ PQR ⦟A = P⦟ ⦟B = Q ⦟By AA similarity criterion△ ABC ∼ △ PQR

Angle Angle Angle (AAA) similarity rule

Two triangles are similar if al l angles of one triangle are equal to corresponding angles of the other triangle.

SINCE , IN △ ABC and △ PQR ⦟A = P⦟ ⦟B = Q⦟ ⦟C = R⦟By AAA similarity criterion△ ABC ∼ △ PQR

A

CB

P

RQ

Side Side Side (SSS) similarity criterionA

CB RQ

P

Two triangles are similar if corresponding sides of both triangle are equal in the same rati o.

SINCE , IN △ ABC and △ PQR AB/PQ BC/QR AC/PRAND ALSO, AB/PQ=BC/QR=AC/PR By SSS similarity criterion△ ABC ∼ △ PQR

TRIANGLESCONGRUENCYCONGRUENCY

RULESSIMILARITY SIMILARITY

RULES SAS ASA, SSS, AAS RHS AA

AAA, SSSAND THAT’S

ALL AND

WHAT YOU HAVE LEARNT ?

ROUND TABLE CONVERSATION

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