Question

In the given figure YH || TE. Prove that ΔWHY ~ ΔWET and also find HE and TE

Answer 1

Statements	Reasons
1. ∠EWT = ∠HWY	Common angle
2. ∠ETW = ∠HYW	Since YH || TE, corresponding angles
3. ∠WET = ∠WHY	Since YH || TE corresponding angles
4. ΔWHY ~ ΔWET	By AAA criteria

Also ΔWHY ~ ΔWET

∴ Corresponding sides are proportionated

`"WH"/"WE" = "HY"/"ET" = "WY"/"WT"`

`6/(6 + "HE") = 4/"ET" = 4/16`

`6/(6 + "HE") = 4/16`

⇒ 6 + HE = `6/4 xx 16`

⇒ 6 + HE = 24

∴ HE = 24 – 6

HE = 18 

Again `4/"ET" = 4/16`

ET = `4/4 xx 16`

ET = 1 × 16

ET = 16