Question

yes by hl
yes by asa
not enough information
yes by aas
yes by sss
yes by sas

Explanation:

⚡ Using what you learned: congruence criteria for triangles (sss, sas, asa, aas, hl)

Step 1: Identify given geometric markings

From the given figure, we observe two right triangles sharing a central vertex where their hypotenuses intersect:

• Both triangles have a right-angle mark (\(90^\circ\)).
• The hypotenuse of each right triangle has a single tick mark, indicating that the hypotenuses are congruent.

Step 2: Identify additional geometric relationships

The two lines intersect to form vertical angles at the center:

• Vertical angles are always congruent.
• This gives us a pair of congruent acute angles opposite to the vertical intersection.

Step 3: Determine the congruence theorem

Let's list the corresponding congruent parts we have established for the two triangles:

1. An Angle (the right angle)
2. An Angle (the vertical angle)
3. A Side (the hypotenuse, which is not between the two angles)

Since we have two angles and a non-included side congruent, we use the Angle-Angle-Side (AAS) congruence criterion.

Answer:

Yes by AAS