Question

Ad= 8cm ae= 6cm eb = 14 cm, and angle aed = angle acb a) prove that triangle ade is similar to triangle abc. (angle aed is 90 degree) show with calculations

calculate the length, in cm, of dc the answer of b is 7cm

Answer 1

To prove that triangle ADE is similar to triangle ABC, compare the corresponding angles and sides. Use the given values to calculate the length of DC in triangle ABC.

Step-by-step explanation:

To prove that triangle ADE is similar to triangle ABC, we need to show that the corresponding angles are equal and the corresponding sides are in proportion.

Since angle AED is given as 90 degrees and angle ACB is equal to angle AED, we know that angle ACB is also 90 degrees.

Now, let's compare the sides. We have AD/AB = 8/14 = 4/7 and AE/AC = 6/14 = 3/7. Since these ratios are equal, we can conclude that triangle ADE is similar to triangle ABC.

To calculate the length of DC, we can use the fact that triangle ADE and triangle ABC are similar. Since the sides are in proportion, we can write DE/BC = AE/AC. Plugging in the values, we have DE/DC = 6/14. Solving for DC, we get DC = (14 * 6)/14 = 6 cm. Therefore, the length of DC is 6 cm.