17 Questions
What is the measure of angle H in the given figure?
40°
What is the measure of angle S in the triangle ∆ROS ≅ ∆CAN?
40°
What is the measure of angle N in the triangle ∆SIT ≅ ∆RUN?
50°
What is the value of $x$ in the triangle ∆MAN ≅ ∆DEN?
30
Which of the following pairs of triangles are congruent according to the given information?
∆MAT ≅ ∆CPU
What is the relationship between the corresponding angles and sides in the congruent triangles ∆MAT and ∆CPU?
∠M ≅ ∠C, ∠A ≅ ∠P, ∠T ≅ ∠U and MA ≅ CP, AT ≅ PU, MT ≅ CU
What is the main objective of the lesson taught in Legazpi City Science High School?
Identifying corresponding parts of congruent triangles
In the given context, what does it mean for two triangles to be congruent?
Their corresponding angles are equal and their sides are equal in length
What is the missing part of the statement '∆𝐼𝑀𝐿 ≅ ∆𝐸𝑅𝐿' based on the given information?
Corresponding angles
How many pairs of triangles are mentioned to be congruent?
Two pairs
What is not a part of the objectives mentioned for the lesson?
Graphing trigonometric functions
If ∠N = 28°, then ∠Z = _____
28°
If ∠I = 92°, then ∠E = _____
92°
If ∠M = 60°, then ∠R = _____
60°
If NI = 4ft, then ZE = _____
4ft
If IM = 3ft, then ER = _____
3 ft
If MN = 4ft, then RZ = _____
4ft
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
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.
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