Скачать или смотреть In the given figure, ABCD is a square and ∠PQR = 90°. If PB = QC = DR, prove that |

In the given figure, ABCD is a square and ∠PQR = 90°. If PB = QC = DR, prove that | #maths
‪@Integralganit‬

Your Queries:-
In the given figure, ABCD is a square and ∠PQR = 90°. If PB = QC = DR, prove that (i) QB = RC (ii) PQ = QR (iii) ZQPR = 45°

Congruency
Congruency is a fundamental concept in geometry that deals with the similarity of two or more shapes. Two shapes are said to be congruent if they have the same size and shape.

Types of Congruency:
1. SSS (Side-Side-Side) Congruency: If three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent.
2. SAS (Side-Angle-Side) Congruency: If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the two triangles are congruent.
3. ASA (Angle-Side-Angle) Congruency: If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, then the two triangles are congruent.
4. AAS (Angle-Angle-Side) Congruency: If two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the two triangles are congruent.

Quadrilateral
A quadrilateral is a four-sided polygon with four vertices and four sides. Quadrilaterals can be classified into different types based on their properties.

Types of Quadrilaterals:
1. Parallelogram: A quadrilateral with opposite sides parallel.
2. Rectangle: A parallelogram with all right angles.
3. Square: A rectangle with all sides equal.
4. Rhombus: A quadrilateral with all sides equal.
5. Trapezium: A quadrilateral with one pair of parallel sides.
6. Kite: A quadrilateral with two pairs of adjacent sides equal.

Properties of Quadrilaterals:
1.Opposite sides: In a parallelogram, opposite sides are equal and parallel.
2.Opposite angles: In a parallelogram, opposite angles are equal.
3.Diagonals: In a parallelogram, diagonals bisect each other.
4.Sum of interior angles: The sum of interior angles of a quadrilateral is 360°.

Theorems:
1. Converse of the Parallelogram Theorem: If the opposite sides of a quadrilateral are equal, then it is a parallelogram.
2.Converse of the Rectangle Theorem: If the opposite sides of a quadrilateral are equal and the diagonals are equal, then it is a rectangle.
3.Converse of the Rhombus Theorem: If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

By understanding these concepts and theorems, students can develop problem-solving skills and apply them to real-world situations

Triangle Congruency:

SSS (Side-Side-Side) congruency
SAS (Side-Angle-Side) congruency
ASA (Angle-Side-Angle) congruency
AAS (Angle-Angle-Side) congruency
HL (Hypotenuse-Leg) congruency
Triangle congruency theorems
Proof of triangle congruency
Applications of triangle congruency

Quadrilateral:

Types of quadrilaterals (parallelogram, rectangle, square, rhombus, trapezium)
Properties of quadrilaterals (opposite sides, opposite angles, diagonals)
Quadrilateral theorems (congruent quadrilaterals, similar quadrilaterals)
Proof of quadrilateral theorems
Applications of quadrilateral theorems

Class 9th CBSE:

CBSE Class 9th mathematics
Triangle congruency Class 9th
Quadrilateral Class 9th
CBSE Class 9th study materials
CBSE Class 9th practice questions

Triangle congruency
Quadrilateral
Geometry
Mathematics
CBSE Class 9th
Study materials
Practice questions
Triangle theorems
Quadrilateral theorems
Proof and applications

1. "triangle congruency theorems Class 9th"
2. "quadrilateral properties and theorems"
3. "CBSE Class 9th mathematics study materials"
4. "triangle congruency proof and applications"
5. "quadrilateral theorems and proof"
6. "Class 9th CBSE mathematics practice questions"
7. "geometry and trigonometry Class 9th"
8. "mathematics study materials for Class 9th"
9. "triangle and quadrilateral problems and solutions"
10. "CBSE Class 9th mathematics revision notes"