Question

determine whether triangles abc and dbe are similar by following these steps. 1. ∠abc is congruent to ∠dbe. 2. to use sas similarity, ab and cb must be proportional to db and eb, respectively. 3. find and simplify this ratio: ab/db = dropdown with 2, 3, 4 check image of triangle with labels: a, b, c, d, e; lengths: ad=10.4, db=5.2, ce=23.4, eb=7.8

Explanation:

Step1: Identify lengths of AB and DB

From the diagram, \( AB = AD + DB = 10.4 + 5.2 = 15.6 \)? Wait, no, wait. Wait, looking at the diagram again: AD is 10.4, DB is 5.2? Wait, no, the segment from A to D is 10.4, D to B is 5.2? Wait, no, maybe AB is AD + DB? Wait, no, maybe I misread. Wait, the triangle: A is the top, D is on AB, E is on CB. So AB is the side from A to B, with D between A and B. So AD is 10.4, DB is 5.2? Wait, no, the length of AB: AD is 10.4, DB is 5.2, so AB = 10.4 + 5.2 = 15.6? Wait, but then DB is 5.2. Wait, no, maybe the length of AB is AD + DB? Wait, no, maybe the diagram shows: A to D is 10.4, D to B is 5.2? Wait, no, the problem is to find AB/DB. Wait, maybe AB is 10.4 + 5.2? Wait, no, maybe I made a mistake. Wait, looking at the diagram again: the side from A to D is 10.4, D to B is 5.2? Wait, no, the segment DB is 5.2, and AB is AD + DB = 10.4 + 5.2 = 15.6? Wait, but then AB/DB = 15.6 / 5.2 = 3? Wait, no, 15.6 divided by 5.2: 5.2 times 3 is 15.6. So AB is 15.6, DB is 5.2, so 15.6 / 5.2 = 3. So the ratio is 3.

Wait, let's check again. The diagram: A---D---B, with AD = 10.4, DB = 5.2. So AB = AD + DB = 10.4 + 5.2 = 15.6. Then DB is 5.2. So AB/DB = 15.6 / 5.2 = 3. So the ratio is 3.

Step2: Calculate the ratio

So AB = 10.4 + 5.2 = 15.6, DB = 5.2. Then \( \frac{AB}{DB} = \frac{15.6}{5.2} = 3 \).

Answer:

3