How would I prove the congruency of these triangles?

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

8 0

Answer:

Step-by-step explanation:

In ΔADC & ΔABC,

Statement Reason

AD = BC Given

∠DAC ≅ ∠ACB {AB // BC , AC is transversal, ⇒ alternate interior angles are equal}

AC = CA Reflexive property

ΔADC ≅ ΔABC SAS congruent

AB = CD CPCT -> Corresponding Part of Congruent Triangles

Andre45 [30]3 years ago

3 0

Answer:

SAS

Step-by-step explanation:

line AB = line CD S = SIDE

AB = CD because the shape is a parallelogram and opposite sides of a parallelogram are equal.

Hence, proved AB = CD

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If AB = 8 and BC = 24, then AC = If AB = 17 and AC = 68, then BC =

Kryger [21]

Answer:

(i) The length of AC is 32 units, (ii) The length of BC is 51 units.

Step-by-step explanation:

(i) Let suppose that AB and BC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:

$AC = AB + BC$

If we know that $AB = 8$ and $BC = 24$ , then:

$AC = 8 + 24$

$AC = 32$

The length of AC is 32 units.

(ii) Let suppose that AB and AC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:

$AC = AB + BC$

$BC = AC - AB$