Consider the two triangles.

How can the triangles be proven similar by the SAS similarity theorem?

Show that the ratios XY/VU and YZ/VW are equivalent, and ∠U ≅ ∠X.

Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.

Show that the ratios UW/ZX and XY/WV are equivalent, and ∠W ≅ ∠X.

Show that the ratios XZ/WU and ZY/WV are equivalent, and ∠U ≅ ∠Z.

SAS Similarity Theorem, States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem there are 3 ways that the triangles be proven similar by the SAS similarity theorem

1) ∠U≅∠X and UV/XY=UW/XZ

2) ∠W≅∠Z and UW/XZ=WV/ZY

3) ∠V≅∠Y and UV/XY=WV/ZY

therefore

Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.

AFOKE88 AFOKE88 · Answer 2 · 2021-11-08T14:47:21+01:00

The triangles be proven similar by the SAS similarity theorem by;

Option B; Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.

SAS Similarity Theorem is a congruence theorem that states that if ratio of two corresponding sides are the same and the included angle for the two triangles are congruent, then both triangles are said to be similar.

From the two given triangles, we can see that;

WV = 60

UV = 50

UW = 40

XY = 40

ZY = 48

ZX = 32

We can see that;

UV/XY = 50/40 = 5/4 and UW/XZ = 40/32 = 5/4

Thus; UV/XY=UW/XZ

Also;

UW/XZ = 40/32 = 5/4

WV/ZY = 60/48 = 5/4

Thus;

UW/XZ = WV/ZY

Also;

UV/XY = 50/40 = 5/4

WV/ZY = 60/48 = 5/4

Thus;

UV/XY = WV/ZY

Also, we see that;

∠U ≅ ∠X

∠W ≅ ∠Z

∠V≅∠Y

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