# 11x1 t08 03 congruent triangles (2011)

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• Congruent Triangles

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)

• Congruent TrianglesIn order to prove congruent triangles you require three pieces of information.Hint: Look for a side that is the same in both triangles first.

TESTS(1) Side-Side-Side (SSS)

(2) Side-Angle-Side (SAS)NOTE:must be included

angle

• (3) Angle-Angle-Side (AAS)

• (3) Angle-Angle-Side (AAS)

• (3) Angle-Angle-Side (AAS)

• (3) Angle-Angle-Side (AAS)

• (3) Angle-Angle-Side (AAS)

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position(4) Right Angle-Hypotenuse-Side (RHS)

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position(4) Right Angle-Hypotenuse-Side (RHS)

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position(4) Right Angle-Hypotenuse-Side (RHS)

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position(4) Right Angle-Hypotenuse-Side (RHS)

• (3) Angle-Angle-Side (AAS)

NOTE:sides must be in

the same position(4) Right Angle-Hypotenuse-Side (RHS)

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB ABASDAS given

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB ABASDAS given SAS common is

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB ABASDAS given SAS common is

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB ABASDAS given SAS common is

• e.g. (1985)

A B

CD

S

In the diagram ABCD is a quadrilateral.The diagonals AC and BD intersect at right angles, and BASDAS

(i) Prove DA = AB ABASDAS given SAS common is

ABSADSA given 90 AASBASDAS matching sides in 'sDA AB

• (ii) Prove DC = CB

• (ii) Prove DC = CB SABDA proven

• (ii) Prove DC = CB SABDA proven ABASDAS given

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

ABCACAB isoscelesin sides

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

ABCACAB isoscelesin sides ABCCB isoscelesin s'

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

ABCACAB isoscelesin sides ABCCB isoscelesin s'

Equilateral TriangleA

B C

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

ABCACAB isoscelesin sides ABCCB isoscelesin s'

Equilateral Triangle ABCBCACAB lequilaterain sides A

B C

• (ii) Prove DC = CB SABDA proven

SAC common is ABASDAS given SASBACDAC matching sides in 'sDC CB

Types Of TrianglesIsosceles Triangle

A

B C

ABCACAB isoscelesin sides ABCCB isoscelesin s'

Equilateral Triangle ABCBCACAB lequilaterain sides

ABCCBA lequilaterain s' 60A

B C

• Triangle Terminology

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

Median: Line joining vertex to the midpoint of the opposite side

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

Median: Line joining vertex to the midpoint of the opposite side

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

Median: Line joining vertex to the midpoint of the opposite side

Right Bisector: Perpendicular drawn from the midpoint of a side

• Triangle Terminology

Altitude: (perpendicular height)Perpendicular from one side passing through the vertex

Median: Line joining vertex to the midpoint of the opposite side

Right Bisector: Perpendicular drawn from the midpoint of a side

• Exercise 8C; 2, 4beh, 5, 7, 11a, 16, 18, 19a, 21, 22, 26

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