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→Identifying congruent shapes
====== [[Identifying congruent shapes]] ======
====== [[Identifying congruent shapes]] ======
Polygons are congruent if they are the same size and shape that is, if their corresponding angles and sides are equal. The activity helps in identifying congruent shapes.
====== [[Shapes that are congruent]] ======
====== [[Shapes that are congruent]] ======
Shapes can be combined together to form congruent shapes. Identifying such shapes for congruence is explored in this activity.
====== [[Congruence of regular geometric shapes]] ======
====== [[Congruence of regular geometric shapes]] ======
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This activity involves in identifying the congruent shapes among the shapes of different geometric shapes.<span></span><span></span>
====Concept # 2. Postulates for congruence of triangles.====
====Concept # 2. Postulates for congruence of triangles.====
Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:
Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:
====== [[Congruence in triangles – SSS Rule]] ======
====== [[Congruence in triangles – SSS Rule]] ======
Investigating the possibility of congruence if three sides of a triangle are congruent.
====== [[Congruence in triangles – SAS Rule]] ======
====== [[Congruence in triangles – SAS Rule]] ======
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Given two sides and an angle of two triangles are equal, are the two triangles congruent? This activity investigates the position of the given angle for the two triangles to be congruent. <span></span><span></span>
====Concept # 4 What are similar triangles?====
====Concept # 4 What are similar triangles?====
Triangles are similar if corresponding sides are in the same ratio and corresponding angles are equal. All regular polygons having the same number of sides are always similar. All squares and equilateral triangles are similar. All congruent figures are similar but all similar figures need not be congruent.
=====Activities # =====
=====Activities # =====
====== [[Introduction to similar triangles|Introduction to similar triangles]] ======
====== [[Introduction to similar triangles|Introduction to similar triangles]] ======
Concept of similarity is introduced and investigated by comparing triangles and their elements.
==== Concept # 5. Tests for similarity ====
==== Concept # 5. Tests for similarity ====
=====Activities #=====
=====Activities #=====
======[[Similarity test - AA postulate]]======
======[[Similarity test - AA postulate]]======
In two triangles, if the angles are equal, then the sides opposite to the equal angles are in the same ratio and hence the two triangles are similar.
==== Solved problems/ key questions (earlier was hints for problems). ====
==== Solved problems/ key questions (earlier was hints for problems). ====