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

You might be interested in

The diagram shows the measurements of a frame into which concrete is poured to make steps. The steps are shaped like rectangular

Ivahew [28]

(6 x 16 x 6) + (14 x 16 x 7)
Answer = B

4 0

3 years ago

Find sin20 if sin 0 = 3; 90° < 0 < 180°

Alex777 [14]

Answer:

$\sin 2 \theta = -\dfrac{4\sqrt 5}{9}$

Step-by-step explanation:

$\text{Given that,}\\\\~~~~~~\sin \theta = \dfrac 23\\\\\implies \sin^2 \theta = \left( \dfrac 23 \right)^2\\\\\implies 1- \cos^2 \theta = \dfrac 49 \\\\\implies \cos^2 \theta = 1 - \dfrac 49 \\\\\implies \cos^2 \theta = \dfrac 59\\\\\implies \cos \theta = \pm\sqrt{\dfrac 59} \\\\\implies \cos \theta = \pm \dfrac{\sqrt 5 }3\\\\\text{Since}~ 90^\circ < \theta < 180^{\circ},~\text{the angle lies in 2nd quadrant}\left(\cos \theta ~\text{is negative}\right).\\\\$

$\text{So,}~ \cos \theta = - \dfrac{\sqrt 5 }{3}\\\\\text{Now,}\\\\\sin 2\theta = 2\sin \theta \cos \theta \\\\\\~~~~~~~~=2 \cdot \dfrac 23 \cdot \left( -\dfrac{\sqrt 5}{3} \right)\\\\\\~~~~~~~~=-\dfrac{4\sqrt 5}{9}$