geometry section 4-3
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SECTION 4-3Congruent Triangles
Thursday, February 2, 2012
ESSENTIAL QUESTIONS
How do you name and use corresponding parts of congruent polygons?
How do you prove triangles congruent using the definition of congruence?
Thursday, February 2, 2012
VOCABULARY
1. Congruent:
2. Congruent Polygons:
3. Corresponding Parts:
Theorem 4.3 - Third Angles Theorem:
Thursday, February 2, 2012
VOCABULARY
1. Congruent: Two figures with exactly the same size and shape
2. Congruent Polygons:
3. Corresponding Parts:
Theorem 4.3 - Third Angles Theorem:
Thursday, February 2, 2012
VOCABULARY
1. Congruent: Two figures with exactly the same size and shape
2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon
3. Corresponding Parts:
Theorem 4.3 - Third Angles Theorem:
Thursday, February 2, 2012
VOCABULARY
1. Congruent: Two figures with exactly the same size and shape
2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon
3. Corresponding Parts: The matching parts between two polygons; Corresponding parts have the same position in each polygon
Theorem 4.3 - Third Angles Theorem:
Thursday, February 2, 2012
VOCABULARY
1. Congruent: Two figures with exactly the same size and shape
2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon
3. Corresponding Parts: The matching parts between two polygons; Corresponding parts have the same position in each polygon
Theorem 4.3 - Third Angles Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles must be congruent
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J ∠B ≅ ∠I
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H
∠D ≅ ∠G
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H
∠D ≅ ∠G ∠E ≅ ∠F
Thursday, February 2, 2012
EXAMPLE 1Show that the polygons are congruent by identifying all of
the congruent corresponding parts. Then write a congruence statement.
AB ≅ JI BC ≅ IH CD ≅ HG
DE ≅ GF EA ≅ FJ
∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H
∠D ≅ ∠G ∠E ≅ ∠F
Since all corresponding parts are congruent, ABCDE ≅ JIHGF
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
∠P ≅ ∠O
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9 IT ≅ GN
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9 x − 2 y = 7.5 IT ≅ GN
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9 x − 2 y = 7.5 IT ≅ GN
x − 2(9) = 7.5
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9 x − 2 y = 7.5 IT ≅ GN
x − 2(9) = 7.5
x − 18 = 7.5
Thursday, February 2, 2012
EXAMPLE 2In the diagram, ∆ITP ≅ ∆GNO. Find the values of x and y.
6 y − 14 = 40 ∠P ≅ ∠O
6 y = 54
y = 9 x − 2 y = 7.5 IT ≅ GN
x − 2(9) = 7.5
x − 18 = 7.5
x = 25.5
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO 2. Vertical Angles
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO 2. Vertical Angles3. ∠M ≅ ∠O
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO 2. Vertical Angles3. ∠M ≅ ∠O 3. Third Angle Theorem
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO 2. Vertical Angles3. ∠M ≅ ∠O 3. Third Angle Theorem
4. LMN ≅PON
Thursday, February 2, 2012
EXAMPLE 3Write a two-column proof.
Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON
Prove: LMN ≅PON
1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN , MN ≅ ON 1. Given2. ∠LNM ≅ ∠PNO 2. Vertical Angles3. ∠M ≅ ∠O 3. Third Angle Theorem
4. LMN ≅PON 4. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Thursday, February 2, 2012
CHECK YOUR UNDERSTANDING
p. 256 #1-8
Thursday, February 2, 2012
PROBLEM SET
Thursday, February 2, 2012
PROBLEM SET
p. 257 #9-23 odd, 29, 36, 39, 49, 53, 55
“I've always tried to go a step past wherever people expected me to end up.” - Beverly Sills
Thursday, February 2, 2012
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