Last Updated on August 27, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 7 Triangles. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Chapter | Triangles |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 9 |

Subject | Maths |

Useful for | Class 9 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 9 Maths Chapterwise Case Study |

### Case Study Questions on Triangles

**Questions**

John recently read a Mathematics experiment. He was keen to perform it on its own. He choosed a long building whose height he want to know, he placed a mirror at ground. He is standing at some distance to the building as well as mirror. John height is 5m and the distance of John from mirror is 12m and distance of building from mirror is also 12m and its height 5m.

On the basis of the above information, solve the following questions.

Q 1. Write two congruent triangles formed in the given figure.

Q 2. Find the distance between top of building and mirror.

Q 3. Find the area of **Î”**AED.

Q4. In the given figures, find the measure of âˆ B’A’C’.

**Solutions**

1. In $\triangle A E D$ and $\triangle B C D$,

$$

\begin{aligned}

& A D=B D=12 m \\

& A E=B C=5 m

\end{aligned}

$$

and $\angle A=\angle B=90^{\circ}$

$$

\therefore \triangle A E D \cong B C D

$$

[By SAS rule]

2. In right angled $\triangle E A D$, use Pythagoras theorem,

$$

\begin{aligned}

E D & =\sqrt{(A E)^2+(A D)^2} \\

& =\sqrt{(5)^2+(12)^2}=\sqrt{25+144} \\

& =\sqrt{169}=13 \mathrm{~m}

\end{aligned}

$$

Hence, the distance between top of building and mirror is 13 m .

3. Area of $\triangle \mathrm{AED}=\frac{1}{2} \times \mathrm{AD} \times \mathrm{AE}$

$$

=\frac{1}{2} \times 12 \times 5=30 \mathrm{~m}^2

$$

4. In $\triangle A B C$ and $\triangle A^{\prime} B^{\prime} C^{\prime}$

$$

\begin{aligned}

& A B=A^{\prime} B^{\prime}=5 \mathrm{~cm} \\

& \angle \mathrm{B}=\angle \mathrm{B}^{\prime}=60^{\circ} \\

& \Rightarrow \angle B A C=\angle B^{\prime} A^{\prime} C^{\prime} \\

& \Rightarrow A x=3 x+15^{\circ} \\

& \Rightarrow \angle B^{\prime} A^{\prime} \mathrm{C}^{\prime}=3 x+15^{\circ} \\

& =3 \times 15^{\circ}+15^{\circ} \\

& =45^{\circ}+15^{\circ}=60^{\circ}

\end{aligned}

$$

### Understanding Triangles

**Triangle: **It is a closed figure formed by three intersecting lines. A triangle has three sides, three angles and three vertices. In DABC, AB, BC

and CA are sides; âˆ A, âˆ B and âˆ C are angles; A, B and C are vertices.

**Congruence of Triangles:** Congruent means equal in all aspects or the figures with same shapes and sizes. The two triangles are said to be congruent, if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle. Congruence is denoted by the symbol ‘â‰…â€™.

**Criteria for Congruence of Triangles:**

- SSS (Side-Side-Side) Congruence: If three sides of a triangle are equal to the three sides of another triangle, then the two triangles satisfy the SSS congruency.
- SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle, then the two triangles satisfy the SAS congruency.
- ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle, then the triangles satisfy the ASA congruency.
- RHS (Right-Hand-Side) Congruence: If the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles satisfy the RHS congruency.

**Some Properties of a Triangle:**

- The sum of three angles of a triangle is 180Â°.
- Angles opposite to equal sides of a triangle are equal.
- Sides opposite to equal angles of a triangle are equal.
- Each angle of an equilateral triangle is of 60Â°.
- The altitude drawn from vertex, it bisects perpendicularly the base of an equilateral and isosceles triangle.

**Some important points:**

- CPCT is a short form of writing corresponding parts of congruent triangles.
- Two geometric figures are said to be congruent, if they are equal in all respects.
- Every triangle is congruent to itself.
- If any two pairs of angles and one pair of corresponding sides are equal, then the two triangles are congruent. This may be called as AAS congruence rule.
- The medians of an equilateral triangle are equal.

### Also check

- Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
- Circles Class 9 Case Study Questions Maths Chapter 9
- Quadrilaterals Class 9 Case Study Questions Maths Chapter 8
- Triangles Class 9 Case Study Questions Maths Chapter 7
- Lines and Angles Class 9 Case Study Questions Maths Chapter 6
- Introduction to Euclidâ€™s Geometry Class 9 Case Study Questions Maths Chapter 5
- Linear Equations in Two Variables Class 9 Case Study Questions Maths Chapter 4
- Coordinate Geometry Class 9 Case Study Questions Maths Chapter 3
- PolynomialsÂ Class 9 Case Study Questions Maths Chapter 2
- Number SystemsÂ Class 9 Case Study Questions Maths Chapter 1

### Topics from which case study questions may be asked

- Triangles
- Congruence of triangles
- Criteria for congruence of triangles
- Properties of triangles

If any two pairs of angles and one pair of corresponding sides are equal, then the two triangles are congruent. This may be called as AAS congruence rule.

Case study questions from the above given topic may be asked.

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### Frequently Asked Questions (FAQs) on Triangles Case Study

#### Q1: What are the different types of triangles based on their sides?

A1: Triangles can be classified into three types based on their sides:**Scalene Triangle:** All three sides have different lengths.**Isosceles Triangle:** Two sides are of equal length.**Equilateral Triangle:** All three sides are of equal length.

#### Q2: How are triangles classified based on their angles?

A2: Based on angles, triangles are classified as:**Acute-Angled Triangle:** All angles are less than 90Â°.**Right-Angled Triangle:** One angle is exactly 90Â°.**Obtuse-Angled Triangle:** One angle is greater than 90Â°.

#### Q3: **What is the criteria for the congruence of triangles?**

A3: The criteria for the congruence of triangles include:**SSS (Side-Side-Side):** All three sides of one triangle are equal to the three sides of another triangle.**SAS (Side-Angle-Side):** Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.**ASA (Angle-Side-Angle):** Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.**AAS (Angle-Angle-Side):** Two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.**RHS (Right angle-Hypotenuse-Side):** The hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle.

#### Q4: **What is the significance of the centroid in a triangle?**

A4: The centroid is the point where the three medians of a triangle intersect. It is the center of mass or the balancing point of the triangle and divides each median in the ratio 2:1, where the longer segment is always closer to the vertex.

#### Q5: What are similar triangles, and how can you identify them?

A5: Similar triangles have the same shape but not necessarily the same size. They can be identified by the following criteria:**AA (Angle-Angle):** If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.**SSS (Side-Side-Side):** If the corresponding sides of two triangles are in proportion, the triangles are similar.**SAS (Side-Angle-Side):** If two sides of one triangle are in proportion to two sides of another triangle, and the included angles are equal, the triangles are similar.

#### Q6: **Are there any online resources or tools available for practicing Triangles case study questions?**

A6: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.