Term
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Definition
| 3 sidesadd to 180 degrees |
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Term
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Definition
| 3 points joining the sides of the triangle |
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Term
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Definition
| 2 sides sharing a common sides |
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Term
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Definition
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Term
| how to find a an angle measure with exterior angles theorem |
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Definition
[image]
8x + 15=(4x + 5)+(3x + 20)
8x + 15 = 7x + 25
8x = 7x + 10
x = 10 |
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Term
| how to solve with collary to the triangle sum therom |
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Definition
Make a sketch. Let x° = m™A.
Then m™B = 2x°.
x° + 2x° = 90° The acute angles of a right triangle are complementary.
x = 30 Solve for x.
So, m™A = 30° and m™B = 2(30°) = 60°. |
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Term
| how to solve with the third angles therom |
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Definition
In the diagram, ™N congruent ™R and ™L congruent ™S.
From the Third Angles Theorem, you know
that ™M £ ™T. So, m™M = m™T.
From the Triangle Sum Theorem,
m™M = 180° º 55° º 65° = 60°.
m™M = m™T Third Angles Theorem
60° = (2x + 30)° Substitute.
30 = 2x Subtract 30 from each side.
15 = x Divide each side by 2. |
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Term
| properties of congruent triangles |
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Definition
REFLEXIVE PROPERTY OF CONGRUENT TRIANGLES
Every triangle is congruent to itself.
SYMMETRIC PROPERTY OF CONGRUENT TRIANGLES
If ¤ABC £ ¤DEF, then ¤DEF £ ¤ABC.
TRANSITIVE PROPERTY OF CONGRUENT TRIANGLES
If ¤ABC £ ¤DEF and ¤DEF £ ¤JKL, then ¤ABC £ ¤JKL. |
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Term
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Definition
POSTULATE 19 Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of a second
triangle, then the two triangles are congruent. |
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Term
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Definition
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are congruent to two
sides and the included angle of a second triangle, then the two triangles
are congruent. |
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Term
| how to use distance formula to prove triangles are congruent with coordianates |
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Definition
Use the SSS Congruence Postulate
to show that ¤ABC £ ¤FGH.
SOLUTION
Because AC = 3 and FH = 3, AC
Æ
£ FH
Æ
. Because AB = 5 and FG = 5,
AB
Æ
£ FG
Æ
. Use the Distance Formula to find the lengths BC and GH.
d = (x2 -ºx1)2
+( y2º-y1)2
d = (x2- ºx1)2
+( y2º-y1)2
BC 472
50
2
GH (6º-1)2
+(5º-2)2
= 32
+52
= 52
+32
= 34 = 34
Because BC = 34 and GH = 34 , BC
Æ
£ GH
Æ
. All three pairs of
corresponding sides are congruent, so ¤ABC £ ¤FGH by the
SSS Congruence Postulate. |
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Term
| Angle-Side-Angle (ASA) Congruence Postulate |
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Definition
If two angles and the included side of one
triangle are congruent to two angles and the
included side of a second triangle, then the
two triangles are congruent. |
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Term
| Angle-Angle-Side (AAS) Congruence Theorem |
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Definition
If two angles and a nonincluded side of one
triangle are congruent to two angles and the
corresponding nonincluded side of a second
triangle, then the two triangles are congruent. |
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