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The ideas in this geometry lesson are taken from the Geometry ebook that I sell at MathMammoth.com. This lesson plan does not contain all the problems the Geometry ebook does.

# Angles with the same vertex and vertical anglesFree lesson plan from HomeschoolMath.net

Look at the picture.  How many angles do you see?
 The angle marked with a single arc is called angle CAB.   The points C and B are points on the two sides of the angle,  and A is the vertex point.  Note how the vertex point A  goes in the middle:  angle CAB. Similarly, the angle marked with the double arc is called  the angle DAC (or angle CAD - but the vertex point  has to be in the middle). The angle DAB is the straight angle in the picture.

The two angles DAC and CAB have the same vertex point A.
The angle DAB is a straight angle, thereby measuring __________ degrees.
Measure the angles DAC and CAB.  DAC = _________;  CAB = __________.

What is the sum of the measures of those two angles?  _____________
What is the sum of the measures of all three angles?  _____________

## Example problem types

1.  Measure all the angles in the pictures, including if there are any straight angles, and mark them on the pictures.  Calculate the sum of the angles.  (Due to measuring errors you might not get the same result in the two pictures.)

 sum of the angles = __________ sum of the angles = __________

2.  Measure the angles DAC and CAB in both pictures.  What is the sum of the two angles?   Why?  In the second picture, measure also the angles DAE and EAB and calculate their sum.

 [Pictures available in the ebook] [Picture available in the ebook] angle DAC = _____ angle CAB = _____ sum of the angles = _______ angle DAC = _____ angle CAB = _____ sum  = _______ angle DAE = _____ angle EAB = _____ sum  = _______

3.   Calculate the angles.  What is the principle you are to use?  Note: do not try to measure, because the pictures are not exact.

 a.  angle ABC = _______ b.  angle DAC = ______

Look at the picture.  How many angles do you see?

These four angles are formed by two lines that intersect or cross each other at one point, A.

Measure the angles DAC and EAB.  DAC = _________;  EAB = __________
Measure the angles DAE and CAB.  DAE = _________;  CAB = __________

What do you notice?

Angles DAC and EAB are vertical angles.  Also angles DAE and CAB are vertical angles.

 Here is another picture of vertical angles. The angles marked with one arc form one pair of vertical angles, and the angles marked with the double arc form another pair of vertical angles. Measure the angles and verify they have the same measure.

4.  Calculate the angles.  Note: do not try to measure, because the pictures are not exact.
[Pictures available in the ebook]

5.  Calculate the angles based on the given information.  Do not measure since the picture is not exact.:
[Pictures available in the ebook]

 New terms to remember: vertical angles

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