Question

Decide if there is enough information to prove each of the following pairs of triangles are congruent.

Justify your answer for each pair of triangles.

Answer 1

Explanation:

1)Yes

In ΔABC and ΔDCE,

AC =CE {GIVEN}

∠ACB = ∠ DCE (Veritcally opposite angles)

BC =CD {GIVEN}

ΔABC ≅ ΔDCE {Side Angle Side - SAS CONGRUENCE}

3) Yes

In ΔRST and ΔVUT,

∠RST = ∠VUT = 90°{GIVEN}

ST =TU {GIVEN}

∠RTS = ∠ VTU (Veritcally opposite angles)

ΔRST ≅ ΔVUT { Angle Side Angle - ASA CONGRUENCE}

4)Yes

In ΔDEF and ΔDHG,

ED = DH {GIVEN}

∠EDF = ∠ GDH (Veritcally opposite angles)

FD = DG {GIVEN}

ΔDEF ≅ ΔDHG {Side Angle Side - SAS CONGRUENCE}

2) NO