====== Unit 11: Parallelograms and Triangles ======
On this page notes of Unit 11 of Mathematics 9 written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq are given.
{{ :matric:9th_science:unit-11-9th-science-ptb.jpg?nolink|Unit 08: Linear Graph and their Application}}
After studying this unit, the students will be able to:
* prove that in a parallelogram
* the opposite sides are congruent,
* the opposite angles are congruent,
* 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.
**Quadrilateral:** A figure formed by four non-collinear points in the plane is called a quadrilateral.
**Parallelogram:** A figure formed by four non-collinear points in the plane is called a parallelogram if its opposite sides are parallel.
**Rectangle:** A figure formed in the plane by four non-collinear points is called a rectangle if\\
(i) its opposite sides are equal in length.\\
(ii) the angle at each vertex is of measure 90 degree.
====Solutions====
* Exercise 11.1 | VIEW [[:matric:9th_science:unit11:11-1|View Online]] | {{ :matric:9th_science:ex11-1-9th-science-ptb.pdf |Download PDF}} NEW
* Exercise 11.2 | VIEW [[:matric:9th_science:unit11?f=matric/9th_science/ex11-2-9th-science-ptb#online_view|View Online]] | {{ :matric:9th_science:ex11-2-9th-science-ptb.pdf |Download PDF}} NEW
* Exercise 11.3 | Added soon
* Exercise 11.4 | Added soon
* Exercise 11.5 | Added soon
* Review Exercise |
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