8.1/2 Flashcards
1st general statement about congruent triangles
Congruent triangles are triangles which have the same shape and size.
1st actual proof drawings
Draw to congruent triangles
Label angles accordingly
Tick sides accordingly
Label edges
1st acc proof statement
Two triangles are congruent if their corresponding sides and angles have the same measure.
First Test for Congruency
SAS/‘Two Sides and an Included Angle’ test
Drawing labelling for 1st test
Label triangles
Tick two corresponding lines
Draw angle for angle in between lines for each
Proof for 1st test
In ‘triangle shape’ABC and ‘triangle shape’DEF, if
|AB| = |DE|
|BC| = |EF|
B = E,
then ‘triangle shape’ABC ~= ‘triangle shape’DEF.
Initial basic proof
If A = D |AB| = |DE|
B = E |AC| = |DF|
C = F |BC| = |EF|,
then ‘triangle shape’ABC ~= ‘triangle shape’DEF.
Statement for 1st test
If two pairs of corresponding sides and the included angles are equal, then the two triangles are congruent.
Second test for congruency
AAS/‘Two Angles and Corresponding Side’ test
Statement for 2nd test
If two pairs of corresponding angles and one pair of corresponding sides are qualified, then the two triangles are congruent.
Drawing labelling for 2nd test
Label triangles
Label corresponding angles
Tick any aside apart from side encapsulated by angles (make sure same on both drawings)
Proof for 2nd test
In ‘triangle shape’ABC and ‘triangle shape’DEF, if
B = E
C = F
|BC| = |EF|,
then ‘triangle shape’ABC ~= ‘triangle shape’DEF.
Third Test for Congruency
SSS/‘Side-Side-Side’ test
Statement for 3rd test
If three pairs of corresponding sides are equal, then the two triangles are congruent.
Drawing labelling for 3rd test
Label triangles
Tick all sides with appropriate marks
Proof for 3rd test
In ‘triangle shape’ABC and ‘triangle shape’DEF, if
|AB| = |DE|
|BC| = |EF|
|AC| = |DF|,
then ‘triangle shape’ABC ~= ‘triangle shape’DEF.
Fourth Test of Congruency
RHS/‘Right angle, Hypotenuse and Side’ test
Statement for 4th test
If two triangles have one pair of equal corresponding right angles, one pair of equal corresponding hypotenuses, and one pair of equal corresponding sides, then the two triangles are congruent.
Drawing labelling for 4th test
Draw triangles
Label triangles es
Draw ticks on hypotenuses and vertical side
Draw right angle sign in both
Proof for 4th test
In ‘triangle shape’ABC and ‘triangle shape’DEF, if
B = E = 90 *
|AC| = |DE|
|AC| = |DF|,
then ‘triangle shape’ABC ~= ‘triangle shape’DEF.
