HSPT Math : Concepts
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #2 : Lines
Examine the above diagram. If 
The two marked angles are same-side interior angles of parallel lines, which are supplementary - that is, their measures have sum 180. We can solve for 
Example Question #33 : Plane Geometry
Examine the above diagram. What is 
By angle addition,
Example Question #1 : Lines
Examine the above diagram. Which of the following statements must be true whether or not 
Four statements can be eliminated by the various parallel theorems and postulates. Congruence of alternate interior angles or corresponding angles forces the lines to be parallel, so
Also, if same-side interior angles or same-side exterior angles are supplementary, the lines are parallel, so
However, 
Example Question #2 : Lines
What is 
Supplementary angles and complementary angles have measures totaling 
Example Question #1 : Lines
Note: Figure NOT drawn to scale.
In the above figure, 
Example Question #31 : Plane Geometry
Two angles which form a linear pair have measures 
Two angles that form a linear pair are supplementary - that is, they have measures that total 
The two angles have measure
and
Example Question #6 : How To Find An Angle
Two vertical angles have measures 
Two vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure. Therefore, we set up and solve the equation
Example Question #5 : Lines
A line 
Evaluate 
When a transversal such as 
Two same-side interior angles are supplementary - that is, their angle measures total 180 - so
We can solve this system by the substitution method as follows:
Backsolve:
Example Question #1 : How To Find An Angle
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the measure of 
The top and bottom angles, being vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure, so
or, simplified,
The right and bottom angles form a linear pair, so their degree measures total 180. That is,
Substitute 
The left and right angles, being vertical angles, have the same measure, so, since the right angle measures 
Example Question #2 : Coordinate Geometry
What is the measurement of 
If you extend the lines of the parellelogram, you will notice that a parellogram is the same as 2 different sets of parellel lines intersecting one another. When that happens, the following angles are congruent to one another:
Therefore,
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