Question

determine the congruence pattern. each pattern will be used once.
10)
11)
12)
13)
14)

Explanation:

Step1: Analyze Problem 10

Identify congruent parts: right angles (90°), two pairs of equal sides (marked with || and ×). So, by Hypotenuse-Leg (HL) or Side-Angle-Side (SAS)? Wait, right triangles, two legs equal (|| and ×), so SAS? Wait, actually, for right triangles, if a leg and hypotenuse are equal, HL. But here, two legs: one pair || (equal), one pair × (equal), and right angle. So SAS: right angle (included angle), two sides. So congruence: SAS? Wait, no, the triangles are right-angled, with one leg equal (||), one leg equal (×), and right angle. So SAS (angle between two sides: right angle). So congruence pattern: SAS? Wait, no, maybe HL? Wait, no, HL is hypotenuse and leg. Here, the hypotenuse is the side with ×? Wait, maybe I missee. Let's recheck: the two triangles have right angles, one leg marked || (equal), one leg marked × (equal), and the hypotenuse? Wait, no, the sides with || are one pair, × are another pair. So in right triangles, if two legs are equal, then by SAS (since right angle is included), the triangles are congruent. So congruence pattern: SAS? Wait, no, maybe HL? Wait, no, HL requires hypotenuse and a leg. Alternatively, maybe AAS? No, let's see the marks. The triangles have right angles, one leg equal (||), one leg equal (×), so SAS (side-angle-side: right angle between the two legs). So congruence: SAS.

Step2: Analyze Problem 11

Triangles have two angles equal (marked angles) and a side? Wait, the triangles: one has angle at A and C, another at D and F? Wait, the triangles: let's see, triangle ABC and DEF. Angle at A and D, angle at C and F, and side? Wait, maybe AAS (angle-angle-side) or ASA (angle-side-angle). Wait, the marks: two angles equal, and a side? Wait, the triangles have two angles equal and a side (maybe the included side? No, maybe AAS). So congruence pattern: AAS or ASA? Wait, if two angles and a non-included side, AAS; included side, ASA. Let's see the diagram: the triangles have two angles equal, and the side opposite one of the angles? Wait, maybe AAS.

Step3: Analyze Problem 12

Triangles: one is a right triangle (marked right angle), another has a side? Wait, triangle with right angle and triangle with two equal sides? Wait, no, the triangles: one has a right angle, another has a side marked, and maybe a side? Wait, maybe HL? Wait, one triangle is right-angled, another has a side equal, and hypotenuse? Wait, no, maybe SAS? Wait, the triangle with right angle has sides, and the other triangle has a side marked with ×. Wait, maybe HL: right triangle, hypotenuse equal (×) and a leg? Wait, maybe I missee. Alternatively, maybe AAS. Wait, the triangles: one has a right angle, another has an angle, and sides. Maybe HL (Hypotenuse-Leg) because one is right-angled, hypotenuse equal (×), and a leg? Wait, the right triangle has a leg, and the other triangle has a side. Maybe HL.

Step4: Analyze Problem 13

Triangles have two sides equal (marked with | and ×) and an included angle? Wait, the triangles: two sides marked (| and ×) and the included angle equal (marked angle). So SAS (side-angle-side: included angle between the two sides). So congruence pattern: SAS.

Step5: Analyze Problem 14

Triangles have two sides equal (marked with | and ×) and a side? Wait, the triangles are connected with a common side? Wait, the diagram shows two triangles with two sides marked equal (| and ×) and a common side? Wait, no, maybe SSS? Wait, three sides: two sides marked (| and ×) and a common side. So SSS (side-side-side: three sides equal). So congruence pattern: SSS.

Answer:

1. SAS (or HL, but likely SAS)
2. AAS (or ASA)
3. HL (or SAS)
4. SAS
5. SSS

(Note: The exact congruence patterns depend on the precise markings, but the above are the most probable based on typical triangle congruence criteria: SSS, SAS, ASA, AAS, HL.)