Tell whether the triangles are similar. Explain.
2 answers:
Answer:
Step-by-step explanation:
We can use the AA Similarity Theorem that says that if two corresponding pairs of angles are congruent then the two triangles are similar.
11.
On the big triangles we are given one angle is 90° , one angle is 51° and
we know that the sum of all angles in a triangle is 180.
Calculate the missing angle in the big triangle:
180 -90-51 = 39°
Also in the picture we see a given angle of 102° that is adjacent to the 39° angle and another missing angle adjacent that form together 180° given the 2 triangles sin on a straight line.
Calculate the third missing angle
180 -39-102 = 39°
The green triangles are similar because of AA Similarity Theorem.
A= 39°=39° angles with same measure are congruent
A=90°=90° all right angles are congruent
12.
We have 2 vertical angles here and we know that vertical angles are congruent. Is given one of the vertical angle is 29° so the other vertical angle is 29° as well.
We are also given an angle of 88° and given that the sum of angles in a Δ is 180° we can find the third angle in that Δ.
180-29-88 = 63°
On the Δ that is on the right side we are given an angle of 91° and an adjacent angle along a straight line so they must form together 180°. 91+89 = 180
So the third angle in the Δ is 180-29-89 = 62.
We can see here that the angles are not congruent so the yellow triangles are NOT similar.
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Answer:
2744 pennies.
Step-by-step explanation:
Let x represent the number of pennies Al have initially.
We have been given that Al agreed to give 3/7 of his pennies to Bev, so number of pennies Bev will get would be .
We are also told that Bev gave 3/7 of what she got from Al to Carl, so number of pennies that Carl will get would be .
Further, Carl gave 3/7 of what he got from Bev to Dani, so number of pennies that Dani will get would be .
We are also told that Dani received 216 pennies. Now, we will equate 216 to and solve for x as shown below:
Therefore, Al have 2744 pennies initially.
Given the following table that gives data from a linear function:
![\begin {tabular} {|c|c|c|c|} Temperature, $y = f(x)$ (^\circ C)&0&5&20 \\ [1ex] Temperature, $x$ (^\circ F)&32&41&68 \\ \end {tabular}](https://tex.z-dn.net/?f=%5Cbegin%20%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%0ATemperature%2C%20%24y%20%3D%20f%28x%29%24%20%28%5E%5Ccirc%20C%29%260%265%2620%20%5C%5C%20%5B1ex%5D%0ATemperature%2C%20%24x%24%20%28%5E%5Ccirc%20F%29%2632%2641%2668%20%5C%5C%20%0A%5Cend%20%7Btabular%7D)
The formular for the function can be obtained by choosing two points from the table and using the formular for the equation of a straight line.
Recall that the equation of a straight line is given by
Using the points (32, 0) and (41, 5), we have:
The formular for the function can be obtained by choosing two points from the table and using the formular for the equation of a straight line.
Recall that the equation of a straight line is given by
Using the points (32, 0) and (41, 5), we have: