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
State whether the two triangles are congruent or not. Justify your answer
For the given pair of triangles state the criterion that can be used to determine the congruency?
In the given figure, AD = CD and AB = CB. Identify the other three pairs that are equal
In the following figure, ∆ARO ≅ ∆ ______.
If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
AAS congruence criterion is same as ASA congruence criterion.
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.
Observe the given figure and state the three pairs of equal parts in triangles ABC and DBC.
- Is ∆ABC ≅ ∆DCB? Why?
- Is AB = DC? Why?
- Is AC = DB? Why?
