Podcast
Questions and Answers
What is the measure of angle H in the given figure?
What is the measure of angle H in the given figure?
What is the measure of angle S in the triangle ∆ROS ≅ ∆CAN?
What is the measure of angle S in the triangle ∆ROS ≅ ∆CAN?
What is the measure of angle N in the triangle ∆SIT ≅ ∆RUN?
What is the measure of angle N in the triangle ∆SIT ≅ ∆RUN?
What is the value of $x$ in the triangle ∆MAN ≅ ∆DEN?
What is the value of $x$ in the triangle ∆MAN ≅ ∆DEN?
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Which of the following pairs of triangles are congruent according to the given information?
Which of the following pairs of triangles are congruent according to the given information?
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What is the relationship between the corresponding angles and sides in the congruent triangles ∆MAT and ∆CPU?
What is the relationship between the corresponding angles and sides in the congruent triangles ∆MAT and ∆CPU?
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What is the main objective of the lesson taught in Legazpi City Science High School?
What is the main objective of the lesson taught in Legazpi City Science High School?
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In the given context, what does it mean for two triangles to be congruent?
In the given context, what does it mean for two triangles to be congruent?
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What is the missing part of the statement '∆𝐼𝑀𝐿 ≅ ∆𝐸𝑅𝐿' based on the given information?
What is the missing part of the statement '∆𝐼𝑀𝐿 ≅ ∆𝐸𝑅𝐿' based on the given information?
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How many pairs of triangles are mentioned to be congruent?
How many pairs of triangles are mentioned to be congruent?
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What is not a part of the objectives mentioned for the lesson?
What is not a part of the objectives mentioned for the lesson?
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If ∠N = 28°, then ∠Z = _____
If ∠N = 28°, then ∠Z = _____
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If ∠I = 92°, then ∠E = _____
If ∠I = 92°, then ∠E = _____
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If ∠M = 60°, then ∠R = _____
If ∠M = 60°, then ∠R = _____
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If NI = 4ft, then ZE = _____
If NI = 4ft, then ZE = _____
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If IM = 3ft, then ER = _____
If IM = 3ft, then ER = _____
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If MN = 4ft, then RZ = _____
If MN = 4ft, then RZ = _____
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Study Notes
Congruent Triangles
- Corresponding parts of congruent triangles are congruent (CPCTC).
- When two triangles are congruent, their vertices can be paired so that corresponding sides and corresponding angles are congruent.
Congruent Triangles Examples
- ∠N ≅ ∠Z, if ∠N = 28°, then ∠Z = 28°
- ∠I ≅ ∠E, if ∠I = 92°, then ∠E = 92°
- ∠M ≅ ∠R, if ∠M = 60°, then ∠R = 60°
- 𝑁𝐼 ≅ 𝑍𝐸, if 𝑁𝐼 = 4ft, then 𝑍𝐸 = 4ft
- 𝐼𝑀 ≅ 𝐸𝑅, if 𝐼𝑀 = 3ft, then 𝐸𝑅 = 3ft
- 𝑀𝑁 ≅ 𝑅𝑍, if 𝑀𝑁 = 4ft, then 𝑅𝑍 = 4ft
Congruent Triangles Properties
- ∠𝐶 ≅ ∠𝑂, 𝐶𝐴 ≅ 𝑂𝐹, ∠𝐴 ≅ ∠𝐹, 𝐴𝐵 ≅ 𝐹𝑋, ∠𝐵 ≅ ∠𝑋, 𝐶𝐵 ≅ 𝑂𝑋
Congruent Triangles Theorems
- Triangle Sum Theorem: ∠x + 30° + 110° = 180°
- ∆𝑴𝑨𝑻 ≅ ∆𝑪𝑷𝑼, ∠M ≅ ∠C, ∠A ≅ ∠P, ∠T ≅ ∠U, 𝑀𝐴 ≅ 𝐶𝑃, 𝐴𝑇 ≅ 𝑃𝑈, 𝑀𝑇 ≅ 𝐶𝑈
Solving for Unknowns
- ∆𝑅𝑂𝑆 ≅ ∆𝐶𝐴𝑁, ∠x = 40°
- ∆𝑆𝐼𝑇 ≅ ∆𝑅𝑈𝑁, ∠T = ∠N, 2n + 10 = 50, n = 20
- ∆𝑀𝐴𝑁 ≅ ∆𝐷𝐸𝑁, solve for x
Studying That Suits You
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Description
This quiz focuses on identifying corresponding parts of congruent triangles, naming congruent triangles, finding the measure of corresponding parts, and relating triangle congruence to real-life situations. Students will complete a table by providing the missing triangle congruence statements.
