Question

question 6 of 25 according to the diagram below, which similarity statements are true? check all that apply. a. △abc∼△bdc b. △abc∼△adc c. △abc∼△adb d. △abd∼△bcd

Explanation:

Step1: Identify right triangles

In △ABC, BD⊥AC, so ∠ADB=∠CDB=90°. Assume △ABC is right-angled at B (∠ABC=90°), a common altitude-to-hypotenuse setup.

Step2: Check AA similarity for A

△ABC and △BDC share ∠C. ∠ABC=∠BDC=90°, so AA similarity holds. A is true.

Step3: Check AA similarity for B

△ABC and △ADC share ∠A, but side ratios (AB/AD≠BC/DC) not equal. B is false.

Step4: Check AA similarity for C

△ABC and △ADB share ∠A. ∠ABC=∠ADB=90°, so AA similarity holds. C is true.

Step5: Check SSS similarity for D

△ABD (1.8,2.4,3) and △BCD (2.4,3.2,4) have equal ratios (3/4). D is true.

Answer:

A. △ABC~△BDC, C. △ABC~△ADB, D. △ABD~△BCD