Suppose is congruent to . List all the other correct ways of expressing this congruence.

Question

Homi · Accepted Answer

When two triangles are congruent, their corresponding corners and sides are exactly the same.

Step 1 — Identify Corresponding Vertices

We are told that $\Delta\text{HEN}$ is congruent to $\Delta\text{BIG}$ . This means the order of the letters tells us which corners match. The first letter of the first triangle matches the first letter of the second. The second letter matches the second. The third letter matches the third.

So, we have these matching pairs: H corresponds to B. E corresponds to I. N corresponds to G.

Diagram 1

Step 2 — List All Other Congruence Statements

We can write the letters of the first triangle in any order. For each order, we must write the letters of the second triangle in the matching order. We already have one way: $\Delta\text{HEN} \cong \Delta\text{BIG}$ . Let us find the other five ways.

Let us write the first triangle as $\Delta\text{HNE}$ .
- H matches B.
- N matches G.
- E matches I. So, $\Delta\text{HNE} \cong \Delta\text{BGI}$ .
Let us write the first triangle as $\Delta\text{EHN}$ .
- E matches I.
- H matches B.
- N matches G. So, $\Delta\text{EHN} \cong \Delta\text{IBG}$ .
Let us write the first triangle as $\Delta\text{ENH}$ .
- E matches I.
- N matches G.
- H matches B. So, $\Delta\text{ENH} \cong \Delta\text{IGB}$ .
Let us write the first triangle as $\Delta\text{NHE}$ .
- N matches G.
- H matches B.
- E matches I. So, $\Delta\text{NHE} \cong \Delta\text{GBI}$ .
Let us write the first triangle as $\Delta\text{NEH}$ .
- N matches G.
- E matches I.
- H matches B. So, $\Delta\text{NEH} \cong \Delta\text{GIB}$ .

Answer

(i) $\Delta\text{HNE} \cong \Delta\text{BGI}$ (ii) $\Delta\text{EHN} \cong \Delta\text{IBG}$ (iii) $\Delta\text{ENH} \cong \Delta\text{IGB}$ (iv) $\Delta\text{NHE} \cong \Delta\text{GBI}$ (v) $\Delta\text{NEH} \cong \Delta\text{GIB}$

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