Download 10/22 Congruence and Triangles notes File

Unit 1B2 Day 2
Do now
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 Tell whether it is possible to create each of the
following:
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acute scalene triangle
obtuse equilateral triangle
right isosceles triangle
scalene equiangular triangle
right scalene triangle
Congruence
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 Informal: Two figures are congruent if they have exactly the same
size and shapes.
 Two figures are congruent if and only if their corresponding parts
are congruent.
 Definition of congruent triangles: all _________ pairs of
corresponding sides congruent; all _________ pairs of
corresponding angles congruent.
Ex. 1: Proving Congruence
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 Are the two triangles congruent? Use the definition
of congruent triangles. If so, write a congruence
statement.
Ex. 1A: Congruent Figures
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In the diagram, NPLM ≅ EFGH. Find the
values of x and y.
Third Angles Theorem
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If two angles of one triangle are
congruent to two angles of another
triangle, then ______________________
__________________________________
Ex. 2: Third Angles Theorem
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Find the value of x.
Ex. 2A
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 In the diagram, ABCD ≅ KJHL. Find the values of x
and y.
Ex. 3: Determining Congruence
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Determine whether the triangles are
congruent. Justify your reasoning.
Ex. 3A
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 Decide whether the triangles are congruent. Justify
your reasoning.
Ex. 4: Proving Congruence
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 Given: AB || DC, AB ≅ DC, E is the midpoint of BC
and AD.
 Prove: ΔAEB ≅ ΔDEC
Properties of Congruent
Triangles
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Reflexive property of congruent triangles:
Every triangle is congruent to ____________.
Symmetric property of congruent triangles:
If ΔABC ≅ ΔDEF, then _________________
Transitive property of congruent triangles:
If ΔABC ≅ ΔDEF and ΔDEF ≅ ΔJKL, then
______________.
Closure
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If ΔGHJ ≅ ΔMNP, what corresponding
angles and sides are congruent?