Download Lesson Plan Template Lesson Summary Triangle congruence

Lesson Plan Template
Lesson Summary Triangle congruence
Grade 12: Circle Geometry
SCO’s :
E11, E4
Assessment
exercice 1 :
http://plans.ednet.ns.ca/sites/default/files/assessment_archive/Resource%20Documents/NSEMathematics-AStudyGuideForStudents.pdf p78
Exercice 2
http://plans.ednet.ns.ca/sites/default/files/assessment_archive/Resource%20Documents/NSEMathematics-AStudyGuideForStudents.pdf p 79
Communication
there will be lots of opportunity during the lesson for students to share ideas,listen to other,ask
questions and explain their thought.student will devellop a new vocabulary list related to the chapter.
Technology
intenet worsheetc.video, calculator.
Materials
calculator,,worksheets
Mental Math
Development (Recall knowledge, Pre-activity, Activity, Post-Activity, etc)
Side- Side-Side (SSS)
Using words:
If 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.
Using labels:
If in triangles ABC and DEF, AB = DE, BC = EF, and CA = FD, then triangle ABC is congruent to triangle DEF.
Proof: This was proved by using SAS to make "copies" of the two triangles side by side so that together
they form a kite, including a diagonal. Then using what was proved about kites, diagonal cuts the kite
into two congruent triangles.
Details of this proof are at this link. The similarity version of this proof is B&B Principle 8.
Angle-Side-Angle (ASA)
Using words:
If two angle in one triangle are congruent to two angles of a second triangle, and also if the included
sides are congruent, then the triangles are congruent.
Using labels:
If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AB = DE, then triangle ABC is
congruent to triangle DEF.
Proof: This proof was left to reading and was not presented in class. Again, one can make congruent
copies of each triangle so that the copies share a side. Then one can see that AC must = DF.
Side-Side-Angle (SSA) not valid in general
Using labels:
SSA would mean for example, that in triangles ABC and DEF, angle A = angle D, AB = DE, and BC = EF.
With these assumptions it is not true that triangle ABC is congruent to triangle DEF. In general there are
two sets of congruent triangles with the same SSA data.
Hypotenuse-Leg (HL) for Right Triangles
There is one case where SSA is valid, and that is when the angles are right angles.
Using words:
In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a
second right triangle, then the triangles are congruent.
Using labels
If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then
triangle ABC is congruent to triangle DEF.
who can sum up what we did today ?
Extensions:
atlantic canada mathematiquescurriculum grade 12;p 132-134 ;exercice 1
Follow-up Activities:
atlantic canada mathematiquescurriculum grade 12;p 132-134 ;exercice 8 and
9
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