Question: State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. △BCD ~ ______ A) similar; AA similarity; △KLB B) similar; SAS similarity; △BKL C) not similar D) similar; SSS similarity; △KLB Graph/shapes: A large triangle with vertices C at left, D at upper right, and B at lower right; point K lies on segment CB near the middle, and point L lies on segment DB. A smaller triangle KLB is drawn inside the large triangle. The base CB is labeled 4, segment KB is labeled 1, and side DB is labeled 2 with a blue double-arrow measurement. position_hint: center

1. **State the problem:** Determine if triangles △BCD and △KLB are similar, and if so, identify the similarity criterion and complete the similarity statement. 2. **Given information:** - Triangle △BCD with vertices B, C, D. - Smaller triangle △KLB inside △BCD. - Segment CB = 4 units. - Segment KB = 1 unit. - Segment DB = 2 units. 3. **Analyze side lengths:** - Since KB = 1 and CB = 4, then CK = CB - KB = 4 - 1 = 3 units. - Side DB = 2 units. 4. **Check ratios of corresponding sides:** - Compare sides in △BCD and △KLB. - Side CB in △BCD corresponds to KL in △KLB. - Side DB in △BCD corresponds to LB in △KLB. 5. **Calculate ratios:** - Ratio of KB to CB is $\frac{1}{4}$. - Ratio of DB to LB is given as 2 to ? (LB length not given explicitly). 6. **Use similarity criteria:** - Since the smaller triangle is inside the larger one and points K and L lie on sides CB and DB respectively, triangles share angle at B. - If two sides are proportional and the included angle is equal, SAS similarity applies. 7. **Conclusion:** - Triangles △BCD and △KLB are similar by SAS similarity. - The similarity statement is $\triangle BCD \sim \triangle KLB$. **Final answer:** Option B) similar; SAS similarity; $\triangle BKL$ (Note: The problem states $\triangle BKL$ in option B, but the smaller triangle is $\triangle KLB$, which is the same triangle with vertices reordered. So the similarity statement is $\triangle BCD \sim \triangle KLB$.