Are triangles △ABCtriangle, A, B, C and △DEFtriangle, D, E, F similar? To answer, try to map △ABCtriangle, A, B, C onto △DEFtriangle, D, E,

Question

Are triangles △ABCtriangle, A, B, C and △DEFtriangle, D, E, F similar? To answer, try to map △ABCtriangle, A, B, C onto △DEFtriangle, D, E, F using the interactive widget.

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Isabella 3 days 2021-10-10T19:31:20+00:00 1 Answer 0

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    2021-10-10T19:32:27+00:00

    Answer:

    From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .  

    Step-by-step explanation:

    Given as :

    To Proof : Triangle Δ ABC and Triangle Δ DEF are similar

    There are three methods for two Triangles to be similar

    A ) SAS  i.e side angle side

    B ) AA i.e angle angle

    C ) SSS i.e side side side

    Now,

    A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar

    So, If in  Δ ABC and  Δ DEF

    ∠ B = ∠ E

    and , \dfrac{AB}{DE} =  \dfrac{BC}{EF}

    Then Δ ABC  \sim Δ DEF

    I.e SAS   similarity

    B ) If two triangles have equal corresponding angles , then triangles are similar .

    So, If in  Δ ABC and  Δ DEF

    ∠ B = ∠ E   and   ∠ A = ∠ D

    Then Δ ABC  \sim Δ DEF

    I.e AA similarity

    C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .

    So, If in  Δ ABC and  Δ DEF

    \dfrac{AB}{DE} =  \dfrac{BC}{EF} = \dfrac{AC}{DF}

    Then Δ ABC  \sim Δ DEF

    I.e SSS similarity

    Hence From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .   answer

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