The Correct Answer and Explanation is:
Here is the transcription of the handwritten Vietnamese text from the image.
Transcription:
Cho ΔABC cân tại A. Trên tia đối của tia AC lấy điểm D, trên tia đối của tia CB lấy điểm E sao cho BD = CE. Kẻ BH ⊥ AD tại H, và CK ⊥ AE tại K.
CMR:
a) ΔBHD ~ ΔCKE
b) ΔAHB ~ ΔAKC
Explanation:
The image contains a handwritten mathematics problem in the Vietnamese language. It is a geometry question intended for a middle or high school level, focusing on proving the similarity of triangles based on a given set of conditions.
The problem begins by defining an isosceles triangle, which is a triangle with two sides of equal length. The statement “Cho ΔABC cân tại A” translates to “Given an isosceles triangle ABC with vertex A,” which implies that the sides AB and AC are equal.
Next, the problem describes the construction of additional points and lines. “Trên tia đối của tia AC lấy điểm D” means “On the ray opposite to ray AC, take a point D.” This extends the line segment AC past point C. Similarly, “trên tia đối của tia CB lấy điểm E” means “on the ray opposite to ray CB, take a point E,” extending the segment CB past B. A key condition is given: “sao cho BD = CE,” meaning the length of the segment BD is equal to the length of segment CE.
Following this setup, two perpendicular lines are drawn. “Kẻ BH ⊥ AD tại H” means “Draw a line from point B that is perpendicular to the line AD, intersecting at point H.” This makes triangle BHD a right-angled triangle. Likewise, “và CK ⊥ AE tại K” translates to “and draw a line from C perpendicular to AE, intersecting at point K,” creating the right-angled triangle CKE.
Finally, the problem asks for proof, indicated by “CMR” (an abbreviation for “Chứng minh rằng,” or “Prove that”). There are two parts to the proof:
a) Prove that triangle BHD is similar to triangle CKE (ΔBHD ~ ΔCKE).
b) Prove that triangle AHB is similar to triangle AKC (ΔAHB ~ ΔAKC).
