Envision Math Grade 8 Volume 1 Chapter 7 Understand And Apply The Pythagorean
Page 372 Exercise 1 Answer
The Pythagorean Theorem is an equation that relates the side lengths of a right triangle, a2+ b2 = c2, where a and b are the legs of a right triangle and c is the hypotenuse.
Pythagoras theorem can be used to find any side of a right angled triangle when other two sides are known.
It can be used to know if a triangle is a right angled triangle or not.
Pythagorean Theorem can be used to solve problems
It can be used to find any side of a right angled triangle when other two sides are known.
Using it we can know whether a triangle is a right angled triangle or not.
Page 375 Exercise 1 Answer
The square root of number y is a number x that satisfies the equation y = x ⋅ x.
The square root of a number is a factor that when multiplied by itself gives the number.
Page 375 Exercise 2 Answer
A line segment that connects two corners but does not form an edge.
We get a diagonal when we join any two corners (called “vertices”) that aren’t already connected by an edge.
A diagonal is a line segment that connects two vertices of a polygon and is not a side.
Page 375 Exercise 3 Answer
The total distance covered by the sides of a polygon is called its perimeter.
We can find the perimeter of any figure by adding all the sides of that figure.
The perimeter of a figure is the distance around it.
Page 375 Exercise 5 Answer
Given: 32 + 42
To simplify the expression.
Find the squares of both the no. and add them.
On simplifying, we get 25.
Page 375 Exercise 6 Answer
Given: 22 + 52
To simplify the expression.
Find the squares of both the no. and add them.
On simplifying, we get 29
Page 375 Exercise 7 Answer
Given: 102 − 82
To simplify the expression.
Find the squares of both the no. and add them.
On simplifying, we get 36
Page 375 Exercise 8 Answer
Given: √81
To find: the square root.
Find the factors of the no.
√81 can be written as √9×9
Therefore,
√81 = √92
Use formula √x2 = x
We get
√81 = 9
The square root is 9
Page 375 Exercise 10 Answer
Given: √225
To find: the square root.
Find the factors of the no.
√225 can be written as √15×15
Therefore,
√225 = √152
Use formula √x2 = x
√225 = 15
The root is 15
Page 375 Exercise 11 Answer
Given:
To determine: the distance between the two points.
Use the formula ∣x2∣−∣x1∣
The first point is (x1,y1)=(2,5)
The second point is (x2,y2)=(7,5)
The distance will be ∣x2∣−∣x1∣
= ∣7∣ − ∣2∣
= 2 units
The distance between the two points is 2 units.