Question

Sketch the overlapping triangles separately,, Use the given information to mark allcongruences. Then tell what theorem or postulate you can use to show that thetriangles are congruent.

Answer 1

Step 1

Given;

`AC\cong BD`
`\begin{gathered} \bar{AB}\cong\bar{AB}(\text{ Reflexive)} \\ \bar{AB}\text{ is the hypotenuse in both triangles} \end{gathered}`

Step 2

In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.

In both triangles Two sides; the hypotenuse and one side are equal. The triangles are also right-angled triangles. Therefore the theorem you can use to show that the triangles are congruent is;

`\text{RHS congruency }theorem\text{/}rule`