State if the two triangles are congruent. If they are, state how you know.

Mathematics

1 answer:

Norma-Jean [14]3 years ago

8 0

Answer:

Yes, both triangles are congruent to each other by SIDE ANGLE SIDE property of congruence.

Step-by-step explanation:

Two triangles are said to be congruent if and only if they have same corresponding angles and sides.

Now, here

Side 1 = Side 2 (given)

Side 3 = Side 4 (given)

Central angle of triangle 1 = Central angle of triangle 2 (Vertically Opposite)

Hence, by the rule of SIDE ANGLE SIDE (SAS) rule of congruence ,

Triangle 1 ≅ Triangle 2

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Please help me find the value of x the answer must be exact

jenyasd209 [6]

Answer:

$x=11$

Step-by-step explanation:

This is a 45°-45°-90° triangle. The two legs are the same length, and the hypotenuse is that length times the square root of two:

$leg=x\\hypotenuse=x\sqrt{2}$

Therefore, the value of x is 11.

You can double-check using the sine ratio:

$sineX=\frac{opposite}{hypotenuse}$

Insert the values:

$sin45=\frac{x}{11\sqrt{2} }$

Insert the equation into a calculator:

$x=11$

:Done

*It's important to know that, when working with trigonometry ratios, the hypotenuse is never considered the adjacent or opposite side, and the 90° angle is never used in the ratios.

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