WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides...

17
WHAT IS A CONGRUENT TRIANGLE??

Transcript of WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides...

Page 1: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

WHAT IS A CONGRUENT TRIANGLE??

Page 2: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Definition

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

Page 3: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

What makes a triangle?

A triangle is composed of 6 parts:3 sides3 angles

If all 6 of these parts are congruent to another triangle, then we can say that the two triangles are congruent.

Page 4: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Visual/Picture

Page 5: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Order Matters!!

It is very important to remember that the order of the congruent parts of triangles matters.

Page 6: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Examples/Models

Page 7: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Non-Examples

Page 8: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Congruent Triangle

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

Page 9: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.
Page 10: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Triangle Congruence

SAS, AAS, ASA, SSS, HL

Page 11: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Shortcuts to congruence

Should we really need to find all 6 parts of a triangle to show they are congruent or can we use shortcuts?

Page 12: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Side-Side-Side

If two triangles have ALL 3 of the same side lengths, then we can say they are congruent by the SSS postulate

side

side

side

Page 13: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Side-Angle-Side

If two triangles have the same side lengths and the same angle measure in-between those sides, the two triangles are congruent by the SAS postulate.

side

angle side

Page 14: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Angle-Side-Angle

If two triangles have 2 congruent angles and a congruent side in-between those angles, then they are congruent by the ASA postulate

angleangle

side

Page 15: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Angle-Angle-Side

If two triangles have 2 congruent angles and a congruent side that isn’t in-between them, then the triangles are congruent by the AAS postulate

angle

angle

side

Page 16: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

What about Angle-Side-Side? Angle-Side-Side is not enough to

prove triangles are congruent. As an easy way to remember

that:

don’t be an and try to useA.S.S.

Page 17: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Hypotenuse-Leg

If the hypotenuse and the same leg of two right triangles are congruent then the two right triangles are congruent.

hypot hypotleg leg


Unit 5 Congruent Triangles - Mr. Naughton Math Class · Unit 5 – Congruent Triangles ... SWBAT Identify congruent figures and corresponding parts. ... Triangles with the exact same

Unit 5 Congruent Triangles - Mr. Naughton Math Class · Unit 5 – Congruent Triangles ... SWBAT Identify congruent figures and corresponding parts. ... Triangles with the exact same

Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

Chapter 2 - Headlee's Math Mansion 4 Outline.d… · Web viewTwo triangles are congruent when all of their corresponding parts are congruent. Example 1: A tower roof is composed of

Chapter 2 - Headlee's Math Mansion 4 Outline.d… · Web viewTwo triangles are congruent when all of their corresponding parts are congruent. Example 1: A tower roof is composed of

SWBAT: Identify Methods of Proving Triangles Congruent DAY 2€¦ · Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides

SWBAT: Identify Methods of Proving Triangles Congruent DAY 2€¦ · Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

7.2 Exploring Similar Polygons - anderson1.k12.sc.us · 1 7.2 Exploring Similar Polygons Similar: •corresponding angles are congruent AND •measures of their corresponding sides

7.2 Exploring Similar Polygons - anderson1.k12.sc.us · 1 7.2 Exploring Similar Polygons Similar: •corresponding angles are congruent AND •measures of their corresponding sides

4-1 Congruent Figures - Uplift · PDF fileTwo polygons are congruent polygons if and only if their corresponding sides are congruent. ... 4-1 Congruent Figures Example 5: Engineering

4-1 Congruent Figures - Uplift · PDF fileTwo polygons are congruent polygons if and only if their corresponding sides are congruent. ... 4-1 Congruent Figures Example 5: Engineering

Congruent Figures Objective: 1) To recognize figures & their corresponding parts.

Congruent Figures Objective: 1) To recognize figures & their corresponding parts.

A C B D FIG 1.1 If two chords of a circle are equal,then their corresponding arcs are congruent and conversely,if two arcs are congruent, then their.

A C B D FIG 1.1 If two chords of a circle are equal,then their corresponding arcs are congruent and conversely,if two arcs are congruent, then their.

4.3 Congruent Triangles We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations.

4.3 Congruent Triangles We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations.

5-4 Congruent Triangles. Congruent Triangles An Introduction to Corresponding Parts.

5-4 Congruent Triangles. Congruent Triangles An Introduction to Corresponding Parts.

4-3 Congruent Triangles You identified and used congruent angles. Name and use corresponding parts of congruent polygons. Prove triangles congruent using.

4-3 Congruent Triangles You identified and used congruent angles. Name and use corresponding parts of congruent polygons. Prove triangles congruent using.

N Corresponding Parts of Congruent Figures

N Corresponding Parts of Congruent Figures

Chapter 4: Congruent Triangles · Chapter 4 Congruent Triangles ... • Lesson 4-3 Identify corresponding parts of congruent triangles. ... has parts that are named using the letters

Chapter 4: Congruent Triangles · Chapter 4 Congruent Triangles ... • Lesson 4-3 Identify corresponding parts of congruent triangles. ... has parts that are named using the letters

NEVER use SSA to prove triangles are congruent!. CPCTC Corresponding Parts of Congruent Triangles are Congruent.

NEVER use SSA to prove triangles are congruent!. CPCTC Corresponding Parts of Congruent Triangles are Congruent.

1. 2 Definition of Congruent Triangles ABCPQR Δ ABC Δ PQR AP B Q C R If then the corresponding sides and corresponding angles are congruent ABCPQR, Δ.

1. 2 Definition of Congruent Triangles ABCPQR Δ ABC Δ PQR AP B Q C R If then the corresponding sides and corresponding angles are congruent ABCPQR, Δ.

CONGRUENT TRIANGLES Indolent Ichabod Two triangles are congruent IF AND ONLY IF all of their corresponding parts are congruent.

CONGRUENT TRIANGLES Indolent Ichabod Two triangles are congruent IF AND ONLY IF all of their corresponding parts are congruent.

7.2Similar Polygons. Identifying Similar Polygons When there is a correspondence between two polygons such that their corresponding angles are congruent.

7.2Similar Polygons. Identifying Similar Polygons When there is a correspondence between two polygons such that their corresponding angles are congruent.

Congruent Triangles An Introduction to Corresponding Parts.

Congruent Triangles An Introduction to Corresponding Parts.

Congruent Triangles In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. This means there.

Congruent Triangles In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. This means there.