Question

Plot the given points on graph paper. Draw $\Delta \mathit{\text{ABC}}$and $\Delta \mathit{\text{DEF}}$. Copy and complete the statement $\Delta \mathit{\text{ABC}}\cong \underset{¯}{?}$.

$\mathit{\text{A}}\left(-\mathbf{1}\text{,}\mathbf{2}\right)$$\mathit{\text{B}}\left(\mathbf{4}\text{,}\mathbf{2}\right)$$\mathit{\text{C}}\left(\mathbf{2},\mathbf{4}\right)$

$\mathit{\text{D}}\left(\mathbf{5},-\mathbf{1}\right)$$\mathit{\text{E}}\left(\mathbf{7}\text{,}\mathbf{1}\right)$$\mathit{\text{F}}\left(\mathbf{10},-\mathbf{1}\right)$

Short answer

$\mathbf{\Delta }\mathit{\text{ABC}}\mathbf{\cong }\underset{\mathbf{¯}}{\mathbf{\Delta }\mathit{\text{FDE}}}$.

Step-by-step solution

Step 1. Plot the diagram.

Plot $A\left(-1,2\right)$, $B\left(4,2\right)$, $C\left(2,4\right)$, $D\left(5,-1\right)$, $E\left(7,1\right)$, $F\left(10,-1\right)$ on the graph paper and draw $\Delta ABC$ and $\Delta DEF$ as:

Step 2. Show the calculation.

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then can say that the corresponding angles and the sides of the triangles are congruent.

In the diagram, if the two triangles are superposed, then it is obtained that,

$\Delta ABC\cong \Delta FDE$

Step 3. State the conclusion.

Therefore, $\Delta ABC\cong \Delta FDE$.