1. show that triangle ABC and xyz in the diagram below are similar
2. If AB is equal to 12 cm XY is equal to 8 cm and XC is equal to 6 cm find BC
To show that triangle ABC and XYZ are similar, we need to prove that their corresponding angles are congruent and their corresponding sides are proportional.
Given:
AB = 12 cm
XY = 8 cm
XC = 6 cm
First, we can see that angle A and angle X are corresponding angles since they are both right angles.
Similarly, angle B and angle Y are corresponding angles as well as angle C and angle Z.
Next, we can use the Side-Angle-Side (SAS) similarity criterion to prove that the triangles are similar.
From the given information, we know that the length of side AC in triangle ABC is the same as the sum of the lengths of sides XY and XC in triangle XYZ.
AC = XY + XC
AC = 8 cm + 6 cm
AC = 14 cm
Now, we can find the length of side BC in triangle ABC using the Pythagorean theorem:
(BC)^2 = (AB)^2 + (AC)^2
(BC)^2 = 12^2 + 14^2
(BC)^2 = 144 + 196
(BC)^2 = 340
BC = √340
BC ≈ 18.44 cm
Therefore, the length of side BC in triangle ABC is approximately 18.44 cm.