Question

state how the triangles are congruent using sss, sas, asa, aas, or hl. if they are not congruent, type not.

(image of triangles with labels a, e, c, d, f)

type your answer...

7 fill in the blank 4 points
state how the triangles are congruent using sss, sas, asa, aas, or hl. if they are not congruent, type not.

(image of triangles with labels l, m, n, o, p, k)

type your answer...

8 fill in the blank 4 points
state how the triangles are congruent using sss, sas, asa, aas, or hl. if they are not congruent, type not.

(image of a rectangle with labels w, z, i, k and a diagonal)

type your answer...

Explanation:

First Triangle (A, E, etc.)

Step1: Identify equal sides

From the diagram, \( AC = CE \) (marked equal), \( AE = DC \) (marked equal), and \( EC \) is common? Wait, no, looking at the first triangle: \( \triangle ACE \) and \( \triangle DCE \)? Wait, no, the first figure: \( \triangle ABC \) (wait, labels: A, B, C, E, D). So \( AC = CE \) (marked with same tick), \( AB = CD \) (marked), and \( BC = CE \)? Wait, no, the first triangle: sides \( AC = CE \) (given by the tick marks on the base), \( AE = DC \) (tick marks on the legs), and the included angle? Wait, no, actually, let's check SSS. \( AC = CE \), \( AE = DC \), and \( EC \) is common? Wait, no, the two triangles are \( \triangle ACE \) and \( \triangle DCE \)? Wait, maybe \( \triangle ABC \) and \( \triangle DCE \). Wait, the first figure: \( AB = CD \) (tick), \( BC = CE \) (tick), and \( AC = DE \) (tick)? Wait, no, the correct congruence: let's see, the base \( AC = CE \) (same tick), the legs \( AB = CD \) (tick), and \( AE = DC \)? Wait, maybe SSS. Wait, the first triangle: sides \( AC = CE \), \( AB = CD \), and \( BC = CE \)? No, maybe the two triangles are \( \triangle ABC \) and \( \triangle DCE \), with \( AC = CE \), \( AB = CD \), and \( BC = CE \)? Wait, no, the correct congruence is SSS because all three corresponding sides are equal (marked with ticks). So the triangles are congruent by SSS.

Step2: Confirm SSS

SSS (Side-Side-Side) congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. Here, the three sides are marked equal, so SSS applies.

Step1: Identify equal sides and vertical angles

We have \( LN = NO \) (tick marks), \( MN = NP \) (tick marks), and \( \angle LNM = \angle ONP \) (vertical angles, equal). So this is SAS (Side-Angle-Side) because two sides and the included angle are equal.

Step2: Confirm SAS

SAS (Side-Angle-Side) congruence: if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, they are congruent. Here, \( LN = NO \), \( MN = NP \), and included angle \( \angle LNM = \angle ONP \) (vertical angles), so SAS.

Step1: Identify right angles and equal sides

The figure is a rectangle? Wait, \( WI \) and \( KZ \) are vertical sides (right angles), \( IK \) and \( WZ \) are horizontal sides. The diagonal \( IZ \) is common. So \( \triangle WIZ \) and \( \triangle KIZ \) are right triangles. \( WI = KZ \) (tick marks), \( IZ = IZ \) (common hypotenuse), so HL (Hypotenuse-Leg) congruence.

Step2: Confirm HL

HL (Hypotenuse-Leg) congruence for right triangles: if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, they are congruent. Here, \( \angle W = \angle K = 90^\circ \), \( WI = KZ \) (leg), \( IZ = IZ \) (hypotenuse), so HL.

Answer:

SSS

Second Triangle (L, M, N, O, P)