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