Question

complete the congruence statement.
defc ≅
submit
learn about congruence!
how can you tell if two figures are congruent?
congruence transformations
congruence statements
triangle congruence: sss, sas, asa, aas, and hl
lesson: congruence

Explanation:

Step1: Identify corresponding vertices

In rectangle DEFC, the vertices are D, E, F, C. In the other rectangle, we need to match the sides. DE is 26 km, EF is 19 km, FC is 26 km, CD is 19 km. Looking at the second rectangle, XU is 19 km, UV is 26 km, VW is 19 km, WX is 26 km. So we match D to U (since CD and XU are 19 km), E to V (EF and UV are 26 km), F to W (FC and VW are 26 km), C to X (DE and WX are 26 km? Wait, no, let's check the order. DEFC: D-E-F-C. So we need to find the rectangle with vertices in order U-V-W-X? Wait, no, let's check the sides. DE is 26, EF is 19, FC is 26, CD is 19. The other rectangle: XU is 19, UV is 26, VW is 19, WX is 26. So the order of DEFC: D (right angle), E (right angle), F (right angle), C (right angle). The other rectangle: X (right angle), U (right angle), V (right angle), W (right angle)? Wait, no, the first rectangle: D and C are top and bottom left, E and F are bottom and top right? Wait, DE is 26 (bottom), EF is 19 (right), FC is 26 (top), CD is 19 (left). The second rectangle: XU is 19 (bottom), UV is 26 (right), VW is 19 (top), WX is 26 (left). So the correspondence: D (bottom left, 90°) corresponds to U (bottom left, 90°), E (bottom right, 90°) corresponds to V (bottom right, 90°), F (top right, 90°) corresponds to W (top right, 90°), C (top left, 90°) corresponds to X (top left, 90°). So DEFC corresponds to UVWX? Wait, no, DEFC: D-E-F-C. So D to U, E to V, F to W, C to X. So DEFC ≅ UVWX? Wait, no, let's check the labels. The second rectangle has vertices X, U, V, W. So X (left bottom), U (right bottom), V (right top), W (left top). So DEFC: D (left bottom), E (right bottom), F (right top), C (left top). So yes, D corresponds to U, E to V, F to W, C to X. So DEFC ≅ UVWX? Wait, no, the problem is DEFC ≅ [what]. Let's check the sides: DE is 26, EF is 19, FC is 26, CD is 19. The other rectangle: XU is 19, UV is 26, VW is 19, WX is 26. Wait, maybe I got the order wrong. Let's list the vertices in order for congruence: the order of the letters in the congruence statement should correspond to congruent vertices. So DEFC: D, E, F, C. So we need to find the rectangle where the first vertex D corresponds to, second E, third F, fourth C. Let's see the angles: all right angles. Sides: DE = 26, EF = 19, FC = 26, CD = 19. The other rectangle: XU = 19, UV = 26, VW = 19, WX = 26. Wait, maybe the correct correspondence is DEFC ≅ UVWX? No, wait, let's check the labels. The second rectangle: X (with right angle), U (right angle), V (right angle), W (right angle). So X to D? No, D has CD = 19 (left side), X has WX = 26 (left side). Wait, maybe I made a mistake. Let's look at the lengths: DE is 26, FC is 26 (top and bottom). EF is 19, CD is 19 (right and left). The other rectangle: WX is 26, UV is 26 (left and right). XU is 19, VW is 19 (bottom and top). So the first rectangle: DE (bottom, 26), EF (right, 19), FC (top, 26), CD (left, 19). The second rectangle: XU (bottom, 19), UV (right, 26), VW (top, 19), WX (left, 26). Wait, so the first rectangle is a rectangle with length 26 and width 19, the second is also a rectangle with length 26 and width 19, but rotated. So the congruence statement: DEFC. Let's list the vertices in order: D, E, F, C. So D is connected to E and C, E to D and F, F to E and C, C to F and D. In the second rectangle, let's find the vertex connected to a 26 km side and a 19 km side. Let's take U: connected to X (19 km) and V (26 km). V: connected to U (26 km) and W (19 km). W: connected to V (19 km) and X (26 km). X: connected to W (26 km) and U (19 km). So D: connected to E (26) and C (19). So D corresponds to U (connected to V (26) and X (19)). E: connected to D (26) and F (19). E corresponds to V (connected to U (26) and W (19)). F: connected to E (19) and C (26). F corresponds to W (connected to V (19) and X (26)). C: connected to F (26) and D (19). C corresponds to X (connected to W (26) and U (19)). So DEFC ≅ UVWX? Wait, no, DEFC: D-E-F-C. So U-V-W-X. So DEFC ≅ UVWX? Wait, but let's check the labels. The second rectangle's vertices are X, U, V, W. So X is top left, U is bottom left, V is bottom right, W is top right? No, the right angles: X has a right angle, U has a right angle, V has a right angle, W has a right angle. So X (left, bottom), U (right, bottom), V (right, top), W (left, top). So D (left, bottom), E (right, bottom), F (right, top), C (left, top). So yes, D=U, E=V, F=W, C=X. So DEFC ≅ UVWX? Wait, but the problem is DEFC ≅ [blank]. Wait, maybe I got the order wrong. Let's check the original figure: DEFC. D to E to F to C. So the sides: DE, EF, FC, CD. In the other figure, the sides are XU, UV, VW, WX. So DE (26) corresponds to UV (26), EF (19) corresponds to VW (19), FC (26) corresponds to WX (26), CD (19) corresponds to XU (19). So the correspondence is D->U, E->V, F->W, C->X. So DEFC ≅ UVWX? Wait, no, DEFC: D-E-F-C. UVWX: U-V-W-X. So yes, DEFC ≅ UVWX? Wait, but let's check the labels again. The second rectangle: X (with 26 km side WX and 19 km side XU), U (19 km XU and 26 km UV), V (26 km UV and 19 km VW), W (19 km VW and 26 km WX). So DEFC: D (19 km CD and 26 km DE), E (26 km DE and 19 km EF), F (19 km EF and 26 km FC), C (26 km FC and 19 km CD). So the correspondence is D=U, E=V, F=W, C=X. Therefore, DEFC ≅ UVWX? Wait, but maybe the correct answer is UVWX? Wait, no, let's see the vertices. The first rectangle: D, E, F, C. The second: X, U, V, W. So DEFC ≅ UVWX? Wait, maybe I made a mistake. Let's try another approach. Congruence of rectangles: corresponding sides equal and corresponding angles equal. So DEFC has sides DE=26, EF=19, FC=26, CD=19. The other rectangle has sides XU=19, UV=26, VW=19, WX=26. So the sides are equal (26 and 19), so they are congruent. Now, the order of the letters in the congruence statement: DEFC. So D corresponds to U, E to V, F to W, C to X. So DEFC ≅ UVWX? Wait, but let's check the labels. The second rectangle is labeled X, U, V, W. So X is connected to W and U, U to X and V, V to U and W, W to V and X. So DEFC: D connected to E and C, E to D and F, F to E and C, C to F and D. So yes, D=U, E=V, F=W, C=X. Therefore, DEFC ≅ UVWX. Wait, but maybe the answer is XUVW? No, the order matters. The congruence statement must have corresponding vertices in order. So DEFC: D-E-F-C. So U-V-W-X. So DEFC ≅ UVWX.

Step2: Confirm the congruence statement

After matching the corresponding vertices based on side lengths and right angles, we see that DEFC corresponds to UVWX.

Answer:

UVWX