Question

assessment: congruent and similar triangles 40 pts

question 37

\\(\delta qst \cong \delta mrp\\) by hl

true
false

Explanation:

Identify the given information

We are given two triangles, \(\Delta QST\) and \(\Delta MRP\).
The diagram shows:

• Side \(SQ\) has a single tick mark, and side \(RM\) has a single tick mark, so \(SQ \cong RM\).
• Side \(ST\) has a double tick mark, and side \(RP\) has a double tick mark, so \(ST \cong RP\).

Analyze the congruence statement

The statement claims:

$$\Delta QST \cong \Delta MRP \text{ by HL}$$

We need to evaluate if this statement is True or False.

Evaluate the HL Congruence Theorem

Using the Triangle Congruence concept, let's recall the requirements for the Hypotenuse-Leg (HL) Congruence Theorem:

1. Both triangles must be right triangles (containing a \(90^\circ\) angle).
2. The hypotenuses must be congruent.
3. One pair of legs must be congruent.

Check the conditions on the given triangles

Looking at \(\Delta QST\) and \(\Delta MRP\):

• There are no right-angle markers (\(90^\circ\) square symbols) at any of the vertices.
• We cannot assume these are right triangles based on visual appearance alone.
• Therefore, the HL (Hypotenuse-Leg) theorem cannot be applied here.

Formulate the final conclusion

Using Geometric Proofs to verify the statement:
Since we do not know if the triangles are right-angled, we cannot prove congruence using the HL theorem. Thus, the statement is False.

Answer:

• True
• False (Correct answer)