"Explain why there is no Addition Property of..." was answered by students like you

High School
Geometry
High school geometry
Congruence

Marilyn Cameron

Answered question

2022-10-13

Explain why there is no Addition Property of Congruence.

Answer & Explanation

Layton Leach

Beginner2022-10-14Added 15 answers

Because congruency deals only with the size of figures not their orientation in the space. For example, two right angles are congruent but if one goes counterclockwise and the other clockwise, then the measure of one right angle is

90^{\circ}

and the measure of the other one is

(- 90^{\circ})

.
By the addition property of congruency, you would have to be able to add the same angle measure to each right angle and have the same result but if you try it, you will see that the results is different:

90^{\circ} + 30^{\circ} = 120^{\circ}

90^{\circ} + 30^{\circ} = - 60^{\circ}

120^{\circ} \neq - 60^{\circ}

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