Pentagons ABCDE and FGHIJ are congruent because their corresponding angles are equal (162, 108, 117, 94, 59 degrees), and corresponding sides have matching lengths (4.1, 3.2, 1.4, 2.2, 2.8 units).
To show that two pentagons are congruent, we need to demonstrate that their corresponding sides are equal in length, and their corresponding angles are equal. In this case, we are given the measures of the angles and the lengths of the sides for the pentagons ABCDE and FGHIJ.
Let's compare the corresponding angles and sides:
1. **Angles:**
- \( \angle A = \angle F \) (Both are 162 degrees)
- \( \angle B = \angle G \) (Both are 108 degrees)
- \( \angle C = \angle H \) (Both are 117 degrees)
- \( \angle D = \angle I \) (Both are 94 degrees)
- \( \angle E = \angle J \) (Both are 59 degrees)
2. **Sides:**
- \( AB = FG = 4.1 \)
- \( BC = GH = 3.2 \)
- \( CD = HI = 1.4 \)
- \( DE = IJ = 2.2 \)
- \( EA = JF = 2.8 \)
Since all corresponding angles are equal, and all corresponding sides are equal, we can conclude that pentagons ABCDE and FGHIJ are congruent. The notation for congruence is often denoted as \( \cong \), so we can write:
\[ \text{Pentagon ABCDE} \cong \text{Pentagon FGHIJ} \]
The probable question may be:
Show that the two pentagons are congruent
given pentagon ABCDE= angle A= 162, angle B= 108, angle C= 117, angle D= 94, angle E= 59. pentagon FGHIJ= FG= 4.1, GH= 3.2, HI= 1.4, IJ= 2.2, JF= 2.8