Advertisements
Advertisements
प्रश्न
In the figure, ∠TMA ≡∠IAM and ∠TAM ≡ ∠IMA. P is the midpoint of MI and N is the midpoint of AI. Prove that ΔPIN ~ ΔATM
Advertisements
उत्तर
Proof:
| S.No. | Statements | Reasons |
| 1. |
∠TMA ≡ ∠IAM ∠TAM = ∠IMA |
given |
| 2. | ∠ATM = ∠IMA |
Remaining angle By angle sum property |
| 3. |
IP = PM ⇒ `"IP"/"PM"` = 1 In = NA ⇒ `"IN"/"NA"` = 1 |
P is the midpoint of IM and N is the midpoint of IA |
| 4. | `"IP"/"PM" = "IN"/"NA"` | By 3 |
| 5. | PN || MA | By 4 |
| 6. |
∠IPN = ∠IMN ∠INP = ∠IAM |
By 5 |
| 7. |
In ΔPIN and ΔATM (i) ∠IPN = ∠TAM (ii) ∠INP = ∠TAM (iii) ∠ATM = ∠PIN |
By 1, 2 and 6 |
| 8. | ΔPIN ∼ ΔATM | By AAA criteria |
APPEARS IN
संबंधित प्रश्न
By applying the ASA congruence rule, it is to be established that ∆ABC ≅ ∆QRP and it is given that BC = RP. What additional information is needed to establish the congruence?
In Fig, can you use the ASA congruence rule and conclude that ∆AOC ≅ ∆BOD?
For the given pair of triangles state the criterion that can be used to determine the congruency?
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the ______.
In the following figure, ∆ARO ≅ ∆ ______.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the following figure, ∠1 = ∠2 and ∠3 = ∠4.
- Is ∆ADC ≅ ∆ABC? Why ?
- Show that AD = AB and CD = CB.
