Solve for x and y: x-3y=-8 3x+2y=31
2 answers:
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Answer:
ASA
Step-by-step explanation:
Given:
Two triangles ABC and EDC such that:
AB ⊥ BD and BD ⊥ DE
C is the midpoint of BD.
The two triangles are drawn below.
Since, AB ⊥ BD and BD ⊥ DE
Therefore, the two triangles are right angled triangle. The triangle ABC is right angled at vertex B. The triangle EDC is right angled at vertex D.
Since, point C is the midpoint of the line segment BD.
Therefore, C divides the line segment BD into two equal parts.
So, segment BC ≅ segment CD (Midpoint theorem)
Now, consider the triangles ABC and EDC.
Statements Reason
1. ∠ABC ≅ ∠CDE Right angles are congruent to each other
2. BC ≅ CD Midpoint theorem. C is midpoint of BD
3. ∠ACB ≅ ∠ECD Vertically opposite angles are congruent
Therefore, the two triangles are congruent by ASA postulate.
So, the second option is correct.
Answer: FH = 16
<h2><u>PART I</u></h2><h2 />Concept:
Bisect means to cut or divide something into two equal parts.
In mathematics, usually bisect means cutting a segment or an angle.
If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.
Solve:
<u>Given information</u>
FG is 16 less than 3 times the length of GH
Let x be the length of GH
<u>Given expression</u>
FG = GH
<u>Set equation</u>
3x - 16 = x
<u>Add 16 on both sides</u>
3x - 16 + 16 = x + 16
3x = x + 16
<u>Subtract x on both sides</u>
3x - x = x + 16 - x
2x = 16
<u>Divide 2 on both sides</u>
2x / 2 = 16 / 2
x=8
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<h2><u>PART II</u></h2><h2><u /></h2>Concept:
In order to find the length of FH, we need to know the idea of the segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
<u>Given information</u>
FG = GH = x
x = 8
<u>Given expression deducted from the segment addition postulate</u>
FH = FG + GH
<u>Substitute values into the expression</u>
FH = x + x
FH = 8 + 8
Hope this helps!! :)
Please let me know if you have any questions
