Question

please give me a answer.ques. 16. in fig. 10.37, ABCD is a rectangle . show that: 1. AC=BD . 2. ∆ DAB=~∆BCD. 3. ∆DAB =~ ∆CBA. ​

Answer 1

Step-by-step explanation:

To solve this problem,you need to know about:

• Congruence of Triangles
• Properties of Rectangles

What are Congruent Triangles?

Two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.

What is the Full Form of CPCT?

CPCT stands for Corresponding parts of Congruent triangles. CPCT theorem states that if two or more triangles which are congruent to each other are taken then the corresponding angles and the sides of the triangles are also congruent to each other.

What are the Rules of Congruency?

There are 5 main rules of congruency for triangles:

SSS Criterion: Side-Side-Side

SSS Criterion: Side-Side-SideSAS Criterion: Side-Angle-Side

SSS Criterion: Side-Side-SideSAS Criterion: Side-Angle-SideASA Criterion: Angle-Side- Angle

SSS Criterion: Side-Side-SideSAS Criterion: Side-Angle-SideASA Criterion: Angle-Side- AngleAAS Criterion: Angle-Angle-Side

SSS Criterion: Side-Side-SideSAS Criterion: Side-Angle-SideASA Criterion: Angle-Side- AngleAAS Criterion: Angle-Angle-SideRHS Criterion: Right angle- Hypotenuse-Side

What is SSS congruency of triangle?

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

What is SAS congruence of triangles?

If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

What is ASA congruency of triangles?

If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

What is AAS congruency?

When two angles and a non-included side of any two triangles are equal then they are said to be congruent.

What is RHS congruency?

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

Properties of Rectangles

Rectangle Properties

The fundamental properties of rectangles are:

• A rectangle is a quadrilateral
• The opposite sides are parallel and equal to each other
• Each interior angle is equal to 90 degrees
• The sum of all the interior angles is equal to 360 degrees
• The diagonals bisect each other
• Both the diagonals have the same length
• A rectangle with side lengths a and b has the perimeter as 2a+2b units
• A rectangle with side lengths a and b has the area as: ab sin 90 = ab square units
• The sum of the interior angles is equal to 360 degrees
• A diagonal of a rectangle is a diameter of its circumcircle

If a and b are the sides of a rectangle, then the length of each diagonal is: d= √a^2+b^2

$\sqrt{ {a}^{2} } + \sqrt{ {b}^{2} }$

• The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle
• If the two diagonals bisect each other at right angles, then the rectangle is known as a square
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangle
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangle

Hope it will help you.

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