Do the following equations have
NS-No Solution
IS- Infinite solutions
OS- One solution
PLEASE COPY AND PASTE THE PROBLEMS WITH THE ANSWERS INTO THE TEXT BOX: Use the abbreviations above for your answers, placing them to the left of the equation.
_____ 1. 4x+9= 5+4+ 4x
_____2. 7y=49
_____3. 5y +8= 8+5y
_____4. 3x + 5= 4x+5
_____5. 2y-5= 2y+10
_____6. 6x+3= 3(2x+1)
Answers
Step-by-step explanation:
1. 4x+9= 5+4+ 4x
4x+9= 9+4x
NS
2. 7y=49
y= 49/7=7
OS
3. 5y +8= 8+5y
NS
4. 3x + 5= 4x+5
3x-4x=5-5
-x= 0
x= 0
OS
5.2y-5= 2y+10
2y-2y= 10-5
0= 5
NS
6. 6x+3= 3(2x+1)
6x+3= 6x+3
NS
Answer:
Given -
BE and CF are 2 equal altitudes.
To find -
That ∆ABC is an isosceles triangle.
Solution -
In ∆BCF and ∆CBE
→ \angle∠ BFC = \angle∠ CBE (Both 90°)
→ BC = BC (common)
→ FC = CB (Given)
\therefore∴ ∆BCF ≈ ∆CBE (RHS rule)
So,
\angle∠ FCB = \angle∠ ECB (CPCT)
Similarly -
AB = AC (Side opposite to the equal angles of a triangle are also equal)
\therefore∴ ∆ABC is an isosceles triangle.
Hence, proved!
Some more rules of a Triangle -
ASA rule
When 2 angles and one side of a Triangle are equal to the 2 angles and one side of another Triangle. Then Triangles are congurent.
SAS rule
When 2 sides and one angle of a triangle are equal to the 2 sides and one angle of another Triangle. Then Triangles are congurent.
SSS rule
If 3 sides of a Triangle are equal to the 3 sides of another Triangle. Then Triangles are congurent.
RHS rule
If in 2 right triangles the hypotenuse and one side of one Triangle are equal to the hypotenuse and one angle of another Triangle. Then Triangles are congurent.
AAS rule
When 2 angles and one sides are equal to 2 angles and one side of a Triangle. Then Triangles are congurent.
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