Similar Triangles, 4

Category: Plane Geometry

"Published in Newark, California, USA"

In the given figure below, a segment joins the midpoints of two sides of a triangle. Find the values of x and y.

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

There are two variables in the given figure which are the sides of a big triangle. We need two equations in order to solve for the values of x and y.

Since a line segment joins the midpoints of two sides of a triangle, then the first working equation is

A small triangle is similar to big triangle because a line segment which is its base that joins the midpoints of two sides of a big triangle is parallel to the base of big triangle. By similar triangles, the second working equation is

  

but   

Therefore, the value of x is

             

and the value of y is

Similar Triangles, 3

Category: Plane Geometry

"Published in Newark, California, USA"

In the given figure below, a segment joins the midpoints of two sides of a triangle. Find the values of x and y.

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

Since a line segment joins the midpoints of two sides of a triangle, then the value of y is
 

 

 

 

A small triangle is similar to big triangle because a line segment which is its base that joins the midpoints of two sides of a big triangle is parallel to the base of big triangle. By similar triangles, the value of x is

Square, Rectangle, and Parallelogram Problems, 18

Category: Plane Geometry

"Published in Vacaville, California, USA"

A parcel of land is 6 ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Since the two diagonals of a parcel are equal, then the parcel is a rectangle in which all sides are perpendicular to each other. If the diagonal is given, then we can solve for the width of a rectangle by Pythagorean Theorem as follows

By completing the square method,

Since the dimensions of a rectangle are all positive values, then we have to choose the positive sign. Hence, the width of a rectangle is

and the length of a rectangle is .

Therefore, the dimensions of a parcel of land are 120 ft by 126 ft.