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2 answers:
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Answer:
ΔABD ≅ ΔACD by SAS, therefore;
by CPCTC
Step-by-step explanation:
The two column proof is presented as follows;
Statement Reason
ABCD is a trapezoid Given
Given
Definition of a trapezoid
ABCD is an isosceles trapezoid Left and right leg are equal
∠BAD ≅ ∠CDA Base angle of an isosceles trapezoid are congruent
Reflexive property
ΔABD ≅ ΔACD By SAS rule of congruency
CPCTC
CPCTC; Congruent Parts of Congruent Triangles are Congruent
SAS; Side Angle Side rule of congruency
A 52-card deck is made up of an equal number of diamonds, hearts, spades, and clubs. Because there are 4 suits, there is a 1/4 chance to draw one of them, in our case, spades.
There are 4 aces in a 52-card deck, so the chance of drawing one is 4/52, or 1/13.
The question asks for the probability of drawing an ace or a spade. Because it uses the word "or," we add the probabilities together. This is because there is a chance of drawing either of the cards; it doesn't have to meet both requirements to satisfy the statement.
However, if the question were to say "and," we would multiply the two probabilities.
Let's add 1/4 and 1/13. First, we can find a common denominator. We can use 52 because both fractions can multiply into it (since the ratio came from a deck of 52 cards as well).
Now we can add them together.
This cannot be simplified further, so the probability is 17 in 52, or 33%.
hope this helps!