Class 9 Math Chapter 11 Question Answer
Handwritten and composed notes Class 9 Math Chapter 11 Question Answer Parallelograms and Triangles of Chapter No.11: Parallelograms and Triangles notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Parallelograms and Triangles for the students of Mathematics Science group of the (9 class) Matriculation and these are according to the paper patterns of all Punjab boards.
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Topics which are discussed in the notes are given below:
- Important notes of Class 9 Math Chapter 11 Question Answer for Matriculation part-I students.
- Complete Multiple Choice Questions (MCQs) of Chapter No.11: Parallelograms and Triangles 9th class Mathematics Science group in English medium.
- Complete Chapter exercise wise solved questions of Chapter No.11: Parallelograms and Triangles 9th class Mathematics Science group in English medium.
- Complete Chapter review exercise questions of Chapter No.11: Parallelograms and Triangles 9th class Mathematics Science group in English medium.
- Important definitions Asking in board question papers of Chapter No.11: Parallelograms and Triangles 9th class Mathematics Science group in English medium.
- Here are the detailed 9th class math chapter 11 question answer pdf to help you prepare for your exams.
- Prove that in a parallelogram: (i) The opposite sides are congruent, (ii) The opposite angles are congruent, (iii) The diagonals bisect each other.
- Prove that if two opposite sides of a quadrilateral are congruent
and parallel, it is a parallelogram.
- Prove that the line segment, joining the midpoints of two sides of
a triangle, is parallel to the third side and is equal to one-half of its
length.
- Prove that the medians of a triangle are concurrent and their point
of concurrency is the point of trisection of each median.
- Prove that if three or more parallel lines make congruent segments
on a transversal, they also intercept congruent segments on any
other line that cuts them.
- You can also download the 9th class math chapter 11 question answer pdf download for free.
- Introduction: Before proceeding to prove the theorems in this unit the students
are advised to recall definitions of polygons like parallelogram,
rectangle, square, rhombus, trapezium etc. And in particular triangles
and their congruency.
- Theorem 11.1.1: In a parallelogram
(i) Opposite sides are congruent.
(ii) Opposite angles are congruent.
(iii) The diagonals bisect each other.
- Construction
In the figure as shown, we label the angles as ∠1, ∠2, ∠3, ∠4,
∠5, and ∠6
- Corollary: Each diagonal of a parallelogram bisects it into two congruent triangles.
- Example: The bisectors of two angles on the same side of a parallelogram
cut each other at right angles.
- To Prove
m ∠ E = 90°
- Construction: Name the angles ∠ 1 and ∠ 2 as shown in the figure.
- 1. One angle of a parallelogram is 130°. Find the measures of its
remaining angles.
- 2. One exterior angle formed on producing one side of a parallelogram
is 40°. Find the measures of its interior angles.
- Theorem 11.1.2: If two opposite sides of a quadrilateral are congruent and
parallel, it is a parallelogram.
- Given
In a quadrilateral ABCD,
AB ≅ DC and ABDC , To Prove
ABCD is a parallelogram
- Construction: Join the point B to D and in the figure, name the angles as indicated:
∠1, ∠2, ∠3, and ∠4
- 1. Prove that a quadrilateral is a parallelogram if its
(a) opposite angles are congruent. (b) diagonals bisect each other.
- 2. Prove that a quadrilateral is a parallelogram if its opposite sides
are congruent.
- Theorem 11.1.3: The line segment, joining the mid-points of two sides of a triangle, is parallel to the third side and is equal to one-half of its
length.
- Given
In ∆ABC, The mid-points of AB and AC are L and M respectively. To Prove
LM || BC and mLM = 1 / 2 mBC. Construction
Join M to L and produce ML to N such that ML ≅ LN. Join N to B and in the figure, name the angles as ∠1, ∠2 and ∠3