Download Math review - Hudson Falls Middle School

Math review
Chapter 4
By: Megan and Destiny
Side angle side
Side side side
Angle side angle
Angle angle side
Proofs
__
__ __
Given: AB ~= DE, C is the midpoint of BD
__
and AE
Prove: ∆ABC =∆EDC
Statements
__ __
1. AB ~= DE,__C is the midpoint
of BD and AE
reasons
1.given
2. BC = DC, AC = EC
2. definition of midpoint
3. ∆ABC =∆EDC
3. sss
CPCTC
• Corresponding Parts of
Congruent Triangles are
Congruent
• works for all congruent triangles
prove:
MLP
NOP
If two sides of a
triangle are
congruent, then the
angles opposite
those sides are
congruent.
 B  C
Statements
Reasons
1.
Given
2.
Each angle has one unique angle bisector.
3.
An angle bisector is a ray whose endpoint is the
vertex of the angle and which divides the angle
into two congruent angles.
4.
5.
6.
Reflexive Property.
SAS
CPCTC
If the hypotenuse and a leg
of one right triangle are
congruent to the hypotenuse
and a leg of another right
triangle, then the triangles
are congruent.
Given: ΔABC is isosceles such
that AB ≅ AC and AD the altitude from A
Prove: ΔABD ≅ ΔACD
STATEMENTS
REASONS
1. AD ⊥ BC
1. Definition of altitude
2. ∠ADB and ∠ADC are right angles2. Definition of perpendicular
3. AB ≅ AC
3. Given
4. AD ≅ AD
4. Reflexive property of congruence
5. ΔABD ≅ ΔACD
5. HL theorem of congruence
COMMON ANGLE