How do you prove that two triangles are similar?
To prove similarity, use the AA, SSS, or SAS criterion: AA: Two angles are equal. SSS: All sides are proportional. SAS: Two sides are proportional, and the included angle is equal.
What are the real-life applications of similar triangles?
Similar triangles are used in: Indirect measurement techniques (e.g., finding heights of buildings). Map scaling and architectural designs.
What are the properties of a right-angled triangle?
In a right-angled triangle, one angle measures 90°, and the Pythagoras Theorem holds: c² = a² + b².
What is the sum of the interior angles of a triangle?
The sum of the interior angles of a triangle is always 180°.
How is the sum of an AP derived?
The sum is derived by pairing terms of the sequence in reverse order, resulting in a simplified formula.
What is the importance of the sum of an AP?
It helps in solving problems involving large sequences without manually adding all terms.
What is the formula for the sum of the first n terms of an AP?
Sn = n/2 [2a + (n-1)d]
How is the nth term derived?
The nth term formula is derived from the general property of AP, where each term is the sum of the first term and a multiple of the common difference.
What is the use of the nth term in AP?
The nth term formula helps to calculate specific terms in a sequence without listing all preceding terms.
What is the nth term of an AP?
It is the formula used to find any term in the sequence: aₙ = a + (n - 1)d.
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