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Baye's Theorem
Law of Total Probability: If B 1 , B 2 , B 3 , .., B n are mutually exclusive and exhaustive events of the sample space S, then for any event A of S. Baye's Theorem: Let S be a sample space. If A 1 , A, A 3 ... A n are mutual..
Law of Total Probability: If B 1 , B 2 , B 3 , .., B n are mutually exclusive and exhaustive events of the sample space S, then for any event A of S. Baye's Theorem: Let S be a sample space. If A 1 , A, A 3 ... A n are mutual..Baye's Theorem Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i ) 0 for all i. Then for any event A which is a subset of We hav..
Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i ) 0 for all i. Then for any event A which is a subset of We hav..Baye's Theorem
In the previous section, we have learnt that i) If A and B are two mutually exclusive events, then ii) Before we state and prove Baye's Theorem, we use the above two rules to state the law of total probability. The law of total probability is useful in proving Baye's h..
In the previous section, we have learnt that i) If A and B are two mutually exclusive events, then ii) Before we state and prove Baye's Theorem, we use the above two rules to state the law of total probability. The law of total probability is useful in proving Baye's h..Theorem:
If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that where 2s = a + b + ..
If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that where 2s = a + b + ..Theorem 3 (S.S.S.) Similarity
If three pairs of corresponding sides are proportional then the two triangles are similar. In D ABC and D PQR, D ABC ~ D PQR The above three theorems are without proof. Such theorems can be called postulates. Now, let us compare similar triangles and congruent triangles: In PQ |..
If three pairs of corresponding sides are proportional then the two triangles are similar. In D ABC and D PQR, D ABC ~ D PQR The above three theorems are without proof. Such theorems can be called postulates. Now, let us compare similar triangles and congruent triangles: In PQ |..Similarity Theorem I (S.A.S.) Similarity
Theorem I (S.A.S.) Similarity - If a pair of corresponding angles are equal and the sides including them are proportional, then the triangles are similar. In D ABC and D PQR, A = P and D ABC ~ D ..
Theorem I (S.A.S.) Similarity - If a pair of corresponding angles are equal and the sides including them are proportional, then the triangles are similar. In D ABC and D PQR, A = P and D ABC ~ D ..Theorem I (S.A.S.) Similarity If a pair of corresponding angles are equal and the sides including them are proportional, then the triangles are similar. In D ABC and D PQR, A = P and D ABC ~ D ..
If a pair of corresponding angles are equal and the sides including them are proportional, then the triangles are similar. In D ABC and D PQR, A = P and D ABC ~ D ..Loci and Concurrency Theorems
Sometimes it is necessary in geometry to specify the location of all points satisfying one or more conditions. For example, location of set of points equidistant from two given points, location of set of points equidistant from a given point etc. This is done by considering a set of points th..
Midpoint Theorem - Test Questions
Question 1 - Question: Show that the quadrilateral, formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus. Answer: Given: P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. To prove: PQRS is a rhombus. Proof: Consider D BAC ( In a triangle ..
Question 1 - Question: Show that the quadrilateral, formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus. Answer: Given: P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. To prove: PQRS is a rhombus. Proof: Consider D BAC ( In a triangle ..Given that ∠8 ≅∠1. Determine which lines, if any, are par..
Given that ∠ 8 ≅ ∠ 1. Determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. => s || t , same-side interior angle theorem or s || t , alternate interior angle theorem or l || m , alternat..
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