+ All Categories
Transcript
  • Congruent Triangles

    The student is able to (I can):

    Identify and prove congruent triangles given

    Three pairs of congruent sides (Side-Side-Side)

    Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

    Two angles and a side (Angle-Side-Angle and Angle-Angle-Side)

    A Hypotenuse and a Leg of a right triangle

  • SSS Side-Side-Side

    If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

    T

    I

    N

    C

    U

    P

    4

    6

    7 4

    6

    7

    TIN CUP

  • Example Given: , D is the midpoint of

    Prove: FRD ERD

    F

    R

    ED

    FR ER FE

    StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

    1. 1. Given

    2. D is midpt of 2. Given

    3. 3. Def. of midpoint

    4. 4. Refl. prop.

    5. FRD ERD 5. SSS

    FR ER

    FE

    FD ED

    RD RD

  • SAS Side-Angle-Side

    If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

    L

    H

    S

    U

    T

    A

    LHS UTA

  • Example Given: , A is the midpoint of

    Prove: FAR EAM F

    R

    AM

    E

    FA EA RM

    StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

    1. 1. Given

    2. FAR EAM 2. Vertical s

    3. A is midpt of 3. Given

    4. 4. Def. of midpoint

    5. FAR EAM 5. SAS

    FA EA

    RM

    RA MA

  • ASA Angle-Side-Angle

    If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

    F

    L

    Y

    B U

    G

    FLY BUG

  • AAS angle-angle-side

    If two angles and a nonnonnonnon----includedincludedincludedincluded side of one triangle are congruent to two angles and a non-included corresponding side of another triangle, then the triangles are congruent.

    The non-included sides mustmustmustmust be corresponding in order for the triangles to be congruent.

    N

    IW

    UO

    Y

    YOU WIN

  • ASS angle-side-side

    (we do not cuss in math class)

    There is no ASS (or SSA) congruence theorem.

    (unless the angle is a right angle see next slide)

  • HL hypotenuse-leg

    If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

    J

    O

    E

    M

    AC

    JOE MAC


Top Related