- The triangles HAY and HBV share the angle at vertex H.
- The angles at vertices A and B are marked as congruent, meaning ∠HAY ≅ ∠HBV.
- Since two angles of triangle HAY are congruent to two angles of triangle HBV (the shared angle H and the marked angles at A and B), the triangles are similar by the Angle-Angle (AA) similarity criterion.
- For similar triangles, the ratios of corresponding sides are equal. The side HA corresponds to HB, and side HY corresponds to HV.
- The length of HY is given as 17, and the length of YB is 16, so the length of HB is HY + YB = 17 + 16 = 33.
- The length of BV is given as 22, so the length of HV is HB + BV = 33 + 22 = 55.
- Set up the proportion using the corresponding sides: HA / HB = HY / HV.
- Substitute the known values: x / 33 = 17 / 55.
- Solve for x by cross-multiplying: 55x = 33 * 17.
- Calculate the right side: 33 * 17 = 561.
- Divide both sides by 55: x = 561 / 55.
- Simplify the fraction: x = 51 / 5.
- Convert to decimal: x = 10.2.
Parent Tip: Review the logic above to help your child master the concept of similar triangle problems worksheet.
