The information given is not enough to prove that triangles PON and BCD are congruent triangles, however, they may be similar triangles based on the AA similarity theorem,
Therefore, the triangles <u>ARE NOT</u> necessarily congruent.
<h3>
What are Congruent Triangles?</h3>
Triangles that are congruent will have pairs of corresponding lengths and angles that are congruent to each other.
Triangles PON and BCD have the following:
∠PON ≅ ∠BCD (one pair of congruent angles)
∠OPN ≅ ∠CBD (one pair of congruent angles).
Thus, the information given is not enough to prove that triangles PON and BCD are congruent triangles, however, they may be similar triangles based on the AA similarity theorem,
Therefore, the triangles <u>ARE NOT</u> necessarily congruent.
Learn more about congruent triangles on:
brainly.com/question/1675117
Answer:
1 = 130° , 2 =50° , 3 = 85°, 4=45°
Step-by-step explanation:
1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}
2 = 180 - 1 { angles on a straight line equals 180}
= 180 -130 = 50°
4 = 180 - 135 = 45° { angles on a straight line equals 180}
3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}
3 = 135-50 = 85°
Note : sum of opposite interior angles equals external exterior angle, let's prove it:
If we look at the triangle at the bottom left, we have :
85, 45 and r { let's denote r as the missing angle}
So 85 + 45 + r = 180° { sum of angles of a triangle}
By simple arithmetic
r = 180 - ( 85+45) = 180 - 130 = 50°
but r + 4 = 180° { sum of angles in a straight line equals 180°}
4 = 180 - 50 = 130°
So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}
Answer:
12.2 feet
Step-by-step explanation:
The key to this problem is trigonometry.
Imagine a right triangle. With a height, 10 ft (representing the tree's height), and a base of 7 ft (representing the horizontal distance to the worm).
Now the hypoteneuse length, or otherwise the distance from the worm is unknown.
So this is where we can use the pythagorean theorem.
here is the hypoteneuse length, and 
and 
are the other lengths of the triangle.
Since we know a and b we can solve for c.
But first we will square root both sides of the equation to get and not 
.
Now just plug in our values for a and b respectively. (It doesn't matter what number replaces a or b, just make sure you are replacing a and b with the 2 known values) Calculate.
Round to the nearest tenth.
feet
The answer is C Opposite Leg over the Adjesent Leg you can remember this because of SOH CAH TOA That means Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj
