Question

29.
30.
31.
32.
33.
34.
35.
36.

Explanation:

Step1: Identify the problem type

The problem involves analyzing geometric figures, likely to determine congruence or properties of triangles. This falls under Geometry (a subfield of Mathematics).

Step2: Analyze each figure (taking problem 29 as an example)

For problem 29, we have two triangles with marked congruent sides (three marks on one side, two marks on another, and vertical angles). By SSS (Side - Side - Side) congruence criterion, if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. Here, the marked sides (with three and two marks) and the common vertical angle - related side (since vertical angles are equal, and the sides are marked congruent) suggest SSS congruence.

(Note: Since the specific question about which figure or what to find is not clear, but assuming it's about triangle congruence, we analyze the markings. For example, in figure 29, the two triangles have two sides with two marks (congruent) and one side with three marks (congruent), and the included angle (vertical angles) is equal, so by SAS or SSS? Wait, the sides with three marks are on a straight line, so they are equal, and the sides with two marks are equal, and the vertical angles are equal. Wait, actually, the two triangles have three sides: one with three marks (equal), one with two marks (equal), and the third side (the one with two marks) is common? No, they are vertical angles, so the included angle between the two - marked and three - marked sides is equal (vertical angles). So by SAS (Side - Angle - Side) congruence, the two triangles are congruent.

If we take problem 30, there are two triangles with a common side, and angles marked. The angle at the common vertex is a straight angle (the marked angle is a right angle? Wait, the figure has a right angle mark? No, the middle angle is a full angle? Wait, no, the two triangles have a common side, and the angles at the base are equal, and the included angle (the middle angle) is a straight angle? No, maybe ASA (Angle - Side - Angle) congruence.

But since the original question is not fully specified, but assuming it's about identifying congruent triangles, we can say that for each figure, we check the congruence criteria (SSS, SAS, ASA, AAS, HL) based on the markings (side marks and angle marks).

Answer:

(Assuming the question is about triangle congruence and taking problem 29 as an example) The two triangles in problem 29 are congruent by SSS (or SAS) congruence criterion due to the marked congruent sides and equal vertical angles. (If a specific figure or question was provided, the answer would be more precise. For example, if asked which figure shows congruent triangles by SSS, the answer would be figure 29.)