Please answer quick! Thank You! Math
2 answers:
Answer:
C and D.
Step-by-step explanation:
We are given that Spencer wrote a paragraph for proving that rectangles are parallelograms with congruent diagonals
We have to find the missing step in Spencer's proof
Proof:
According to the given information quadrilateral RECT is a rectangle. By definition of a rectangle , all four angles measure
.Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the converse of the same- side Interior Angles Theorem.
Converse of the same- side angles theorem: When the sum of same side interior angles of a transversal line is then the lines are parallel.
Quadrilateral RECT is then a parallelogram by definition of a parallelogram .Now, construct diagonals ET and CR. Because RECT is a parallelogram ,opposite sides are congruent.Therefore, one can say that segment ER is congruent to segment CT.Segment TR is congruent to itself by the reflexive Property of equality.The Side-Angle-Side(SAS) Theorem says triangle ERT is congruent to triangle CTR.And because corresponding parts of congruent triangles are congruent (CPCTC),diagonals ET and Cr are congruent.
Answer :Option C and D
Converse of the same-Side Interior angles Theorem
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Answer:
The probability is 1/30 or 0.0333
Step-by-step explanation:
For calculating the probability we need to make a division between the number of ways in which the first boy born is named Sam and the second boy born is named Mark and the total number of ways in which the couple can name their children.
To calculate the total number of ways in which the couple can name their children, we can use the rule of multiplication as:
<u> 6 </u> * <u> 5 </u> = 30
First boy Born 2nd Boy Born
Because we have 6 options for the name of the first boy and 5 options for the name of the second boy.
Additionally, In just one option from this 30, the first boy is named Sam and the second is named Mark.
So, the probability is calculate as the division between 1 and 30 as: