Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. 2 parallel horizontal lines are interse
cted by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank. Which statement is true about angles 3 and 5? They are acute. They are congruent. They are complementary. They are supplementary.
2 answers:
Answer:
"They are supplementary" ⇒ last answer
Step-by-step explanation:
* <em>Look to the attached figure</em>
- Two parallel horizontal lines are intersected by a third line
- The angles formed form intersection are labeled on the figure
- From the two parallel lines and
∠5 ≅ ∠1 ⇒ corresponding angles
m∠5 = m∠1
- A linear pair is two angles that are adjacent and form a line and
they are supplementary
∠1 and ∠3 form a line
∠1 and ∠3 are linear pair
* <em>lets prove that ∠3 and ∠5 are supplementary</em>
∵ m∠1 = m∠5 ⇒ corresponding angles
∵ ∠1 and ∠3 form a linear pair
∵ Linear pair are supplementary
∴ m∠1 + m∠3 = 180°
- By substitute ∠1 by ∠5
∴ m∠5 + m∠3 = 180
∴ ∠5 and ∠3 are supplementary
* The true statement is "They are supplementary"
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Answer:
Step-by-step explanation:
Step 1: Pythagoras Theorem
Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:
Step 2: Trigonometric Functions
Only for a right angle triangle following three trigonometric relations are valid
Step 3: Verifying all the possible answers
A: Since, LN = x and using
we can calculate
therefore, NM = x (true)
B: As NM = x therefore it can not be equal to .
C: Using Pythagoras Theorem
It can also be proved using trigonometric relation
As,
Therefore
D and E:
Using same approach similar to part A
Since, LN = x and NM = x
we can calculate
Therefore, and not equal to
1. Draw an accurate picture of the triangle in
the coordinate axes, as shown in the attached picture.<span>
<span>2. Circumscribe a rectangle about the triangle, as shown in
the picture. The coordinates of the points M, N, T are easily identifiable as shown in the
picture.</span>
<span>3. The area of the triangle ABC is The area of
the rectangle - Area 1- Area 2- Area 3.</span>
Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>
<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>
<span>Area rectangle= 7*7=49 (units squared)</span>
<span>Answer: Area of triangle is 20 units squared.</span></span>
