Advertisements
|

NCERT Solutions For Class 9 Maths Chapter 5 Triangles Ex 5.2

Here, Below you all know about NCERT Solutions for Class 9 Maths Chapter 5 Triangles Ex 5.2 Question Answer. I know many of you confuse about finding this Chapter 5 Triangles Class Ex 5.2 Of 9 NCERT Solutions. So, Read the full post below and get your solutions.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 9
SubjectMaths
ChapterChapter 5
ExerciseClass 9 Chapter 5 Triangles Exercise 5.2
Number of Questions Solved8
NCERT Solutions For Class 9 Maths Chapter 5 Triangles Ex 5.2

NCERT Solutions for Class 9 Maths Chapter 5 Triangles Ex 5.2

NCERT TEXTBOOK EXERCISES

Question 1. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at 0. Join A to 0. Show that

(i) OB = OC
(ii) AO bisects ∠A

Solution:

(i) In ∆ ABC, we have
AB = AC (Given)
⇒ ∠B = ∠C
(∵ Angles opposite to equal sides are equal)

Question 2. In ∆ ABC, AD is the perpendicular bisector of BC (see figure). Show that ∆ ABC is an isosceles triangle in which AB = AC.

Solution:

In ∆ABD and ∆ACD, we have ,
DB = DC
∠ ADB = ∠ ADC (∵ D bisect SC)
and AD = AD (Common)
∴ ∆ ABD ≅ ∆ACD (By SAS congruence axiom)
⇒ AB = AC (By CPCT)
Renee,∆ ABC is an isosceles triangle.

Question 3. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see figure). Show that these altitudes are equal.

Solution:

In ∆ ABE and ∆ ACF, we have
∠ AEB = ∠ AFC (BE ⊥ AC, CF ⊥ AS, each 90°)
∠ A = ∠ A (Common)
and AS = AC (Given)
∴ ∆ABE ≅ ∆ACF (By AAS congruence axiom)
⇒ BE = CF (By CPCT)

Question 4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see figure). Show that.

(i) ∆ABE = ∆ACF
(ii) AB = AC i.e., ABC is an isosceles triangle.

Solution:

In ∆ABE and ∆ACF, we have
∠ AEB = ∠ AFC (Each 90°)
∠ BAE = ∠ CAF (Common)
and BE =CF (Given)
∴ ∆ABE ≅ ∆ACF (By AAS congruence axiom)
∴ AB = AC
So, ∆ABC is isosceles.

Question 5. ABC and DBC are isosceles triangles on the same base BC (see figure). Show that ∠ ABD = ∠ACD.

Solution:

In ∆ABC, we have
AB=AC (∵ AABC is an isosceles triangle)
∴ ∠ ABC = ∠ ACB …(i)
(∵ Angles opposite to equal sides are equal)
In ∆ DBC, we have
BD = CD (∵ ADBC is an isosceles triangle)
∴ ∠ DBC = ∠ DCB …(ii)
(∵ Angles opposite to equal sides are equal)
On adding Eqs. (i) and (ii), we have .
∠ ABC + ∠ DBC = ∠ ACB + ∠ DCS
⇒ ∠ ABD = ∠ ACD

Question 6. ∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure). Show that ∠ BCD is a right angle.

Solution:

Question 7. ABC is a right angled triangle in which ∠ A = 90° and AB = AC, find ∠ B and ∠ C.

Solution:

We have, ∠A = 90° (Given)

AB = AC (Given)
⇒ ∠B = ∠C
(∵ Angles opposite to equal sides are equal)
Now, we have
∠A+∠B+∠C = 180° (By ∆ property)
90° + ∠B+ ∠B = 180°
⇒ 2 ∠B = 90°
⇒ ∠B = 45°
∴ ∠B = ∠C = 45°

Question 8. Show that the angles of an equilateral triangle are 60° each.

Solution:

Let ∆ ABC be an equilateral triangle, such that

AB = BC = CA (By property)
Now, AB = AC
⇒ ∠B = ∠C …..(i)
(∵Angles opposite to equal sides are equal)
Similarly, CB = CA
⇒∠A = ∠B …(ii)
(∵ Angles opposite to equal sides are equal)
From Eqs. (i) and (ii), we have
∠A=∠B=∠C …(iii)
Now, ∠A+ ∠B+ ∠C = 180° (By ∆ property)
∠A + ∠A + ∠A = 180° [From Eq. (iii)]
3 ∠A = 180°
∠A = 60°
Hence, ∠ A = ∠B = ∠C = 60°

NCERT Solutions for Class 9 Maths Chapter 5 Triangles Exercise 5.2 PDF

For NCERT Solutions for Class 9 Maths Chapter 5 Triangles Ex 5.2, you may click on the link below and get your NCERT Solutions for Class 9 Maths Chapter 5 Triangles Exercise pdf file.

CLICK HERE

Finally, You all know about NCERT Solutions for Class 9 Maths Chapter 5 Triangles Ex 5.2. If you have any questions, then comment below and share this post with others.

Other Chapter of Class 9 Maths Chapter 5 Triangles

Similar Posts

Leave a Reply

Your email address will not be published. Required fields are marked *