The ratios of corresponding sides in the two triangles are equal. What other information is needed to prove that △FGE ~ △IJH by
the SAS similarity theorem? ∠F ≅ ∠J ∠I ≅ ∠F ∠E ≅ ∠H ∠G ≅ ∠I
2 answers:
solution: option B and C both are correct i.e., option C is correct i.e., ∠E ≅∠H and ∠I ≅ ∠F .
option C is correct i.e., ∠E ≅∠H.
explanation:
it is given that ratio of corresponding sides of ΔFGE and ΔIJH are equal
i.e.,
and if ∠E ≅ ∠H
Then ΔFGE and ΔIJH are similar by SAS (side angle side) similarity theorem.
so option C is correct i.e., ∠E ≅ ∠H.
and option B is also correct
explanation:
since it is given that
And if ∠I ≅ ∠F
then ΔFGE and ΔIJH are similar by SAS (side angle side) similarity theorem.
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It is given that there are 4 cards with numbers 2, 5, 6, and 8.
1) It is required to list all the numbers available when two cards are drawn one after the other and the second card is placed at the right of the first card drawn.
To do this, find the sample space of the draw which are:
Hence, the required numbers.
2) Recall that probability is the ratio:
From the numbers listed, notice that the total number of possible outcomes is 12.
Since event A is "obtained number is even", notice that the number of even numbers in the listed numbers is 9 (26,28,52,56,58,62,68,82,86).
Hence, the number of favorable outcomes is 9.
Substituting into the probability ratio gives the required probability:
Check the number of numbers that are a multiple of 5, notice that they are 3 (25,65,85).
Hence, the required probability of event B is:
The number of multiple of 3 in the listed numbers is 0 since there is no number that is a multiple of 3.
Hence, the required probability of event C is:
Answers:
1) {25,26,28,52,56,58,62,65,68,82,85,86}
2) P(A) = 3/4
P(B) = 1/4
P(C)= 0