CONGRUENCY AND SIMILARITY Identifying congruent and similar shapes

CONGRUENCY AND SIMILARITY Identifying congruent and similar shapes Grade 2 Tara Campbell 11/7/10

Menu Page � Congruence � Definition � Examples � More in Depth � Similarity � Definition � More in Depth � Quiz � Question � 1 2 3 Congratulations you’ve completed congruence!

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Congruent Figures or angles that have the same size and shape Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.

Try it out Study these two triangles. How are they alike?

If we rotated the pink triangle and slid it on top of the green one, the two would fit on top of each other exactly. All the sides and all the angles are equal, so these two triangles are congruent.

More in Depth If two figures are congruent, then their corresponding parts are congruent. Let's look at the corresponding parts of triangles ABC and DFE. A triangle has three sides and three angles. If two triangles are congruent, then the sides and angles that match are called corresponding parts. Here, angle A corresponds to angle D, angle B corresponds to angle F, and angle C corresponds to angle E. Side AB corresponds to side DF, side BC corresponds to side FE, and side CA corresponds to side ED. Congruent figures are named in the order of their corresponding parts. For these triangles, we say "triangle ABC is congruent to triangle DFE, " not "triangle DEF, " because vertex A corresponds to vertex D, vertex B corresponds to vertex F, and vertex C corresponds to vertex E. D A B C F E

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Similarity Geometrical figures that are not necessarily the same size but are the same shape. Figures that are the same shape but not necessarily the same size are called similar figures.

M In Depth H O E N S Let's look at the corresponding parts of these two triangles, triangle MHS and triangle ONE. Are the corresponding sides equal? How about the corresponding angles? These triangles are not congruent, because the corresponding sides are obviously not equal. But they are somehow alike, aren't they? They have the same shape. What about their angles? Are they equal? If we put triangle ONE on top of triangle MHS, we could compare each angle, and we would find that the corresponding angles are all congruent. This gives us the definition of similar triangles: if the corresponding angles of two triangles are congruent, then the triangles are similar.

Question 1 this way

How are these figures related? A. Congruent B. Similar but not Congruent C. Neither similar nor congruent

GREAT JOB! YOU ARE AWESOME! Move on

How are these figures related? A. Congruent B. Similar but not congruent C. Neither similar nor congruent

GREAT JOB! YOU ARE AWESOME! Next Question

Look at this shape: Which one is congruent? A. B. C. A. B. Which one is similar? A. B. C.

GREAT JOB! YOU ARE AWESOME! Now try part B Move on

Sorry Try Again! Go back to #1 Go back to #2 Go back to #3 A Go back to #3 B

Credits…. http: //www. ixl. com/math/practice/grade-3 -similar-and-congruent http: //en. wikipedia. org/wiki/Congruence_(geometry) http: //www. math. com/homeworkhelp/Geometry. html http: //mrsdell. org/geometry/congruence. html http: //www. ncpublicschools. org/curriculum/mathematics/scos/2003/k-8/16 grade 2 Continue on