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Informally, we can say that congruent triangles will be the same shape and the same size. Our mathematical definition for congruency is that corresponding pairs of angles are equal and corresponding sides are equal. Congruent Triangles – Build similar triangles by combining sides and angles. Geoboard – Use geoboards to illustrate area, perimeter, and rational number concepts. Geoboard - Isometric – Use geoboard to illustrate three-dimensional shapes. Ladybug Leaf – Program a ladybug to hide behind a leaf. What consecutive triangle parts need to be congruent in order to show that two triangles are congruent? These applets allow students to explore whether triangle relationships (SSS, AAA, SAS, HL, SSA, ASA, AAS) force triangles to be congruent or not. Are you able to create a non-congruent pair of triangles? And to figure that out, I'm just over here going to write our triangle congruency postulate. So we know that two triangles are congruent if all of their sides are the same-- so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.

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# Congruent triangles are similar or not

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If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal.

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Two triangles are similar if all three of their corresponding pairs of angles are congruent (two pairs of corresponding angles being congruent is enough because all angles of a triangle add to 180 degrees). This is called AA similarity. Corresponding parts of congruent ﬁgures are congru-ent, a theorem that is used often in the proofs of this paper. Congruency of triangles is denoted 4ABC˙4XYZ. A less strong, but frequently useful, statement to make about triangles is that they are similar. Two triangles are similar if the three angles of one are congruent to the three congruent triangles. • Lessons 4-4 and 4-5 Test for triangle congruence using SSS, SAS, ASA, and AAS. • Lesson 4-6 Use properties of isosceles and equilateral triangles. • Lesson 4-7 Write coordinate proofs. Triangles are found everywhere you look. Triangles with the same size and shape can even be found on the tail of a whale.

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