{"id":275404,"date":"2025-07-28T19:16:02","date_gmt":"2025-07-28T19:16:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=275404"},"modified":"2025-07-28T19:16:06","modified_gmt":"2025-07-28T19:16:06","slug":"the-population-of-a-town-is-2500-and-is-decreasing-at-a-rate-of-35-per-year-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/the-population-of-a-town-is-2500-and-is-decreasing-at-a-rate-of-35-per-year-2\/","title":{"rendered":"The population of a town is 2500 and is decreasing at a rate of 3,5% per year."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer<\/strong><\/p>\n\n\n\n

Here is the transcription of the handwritten Vietnamese text:<\/p>\n\n\n\n

B\u00e0i 6:<\/strong> Cho \u0394ABC c\u00e2n t\u1ea1i A.
Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia BC l\u1ea5y \u0111i\u1ec3m D, tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia CB l\u1ea5y \u0111i\u1ec3m E sao cho BD = CE.
K\u1ebb BH \u22a5 AD t\u1ea1i H. K\u1ebb CK \u22a5 AE t\u1ea1i K.
CMR:
a) \u0394BHD = \u0394CKE
b) \u0394AHB = \u0394AKC<\/p>\n\n\n\n

English Translation<\/strong><\/p>\n\n\n\n

Problem 6:<\/strong> Given an isosceles triangle ABC with vertex A.
On the ray opposite to the ray BC, take point D. On the ray opposite to the ray CB, take point E such that BD = CE.
Draw BH perpendicular to AD at H. Draw CK perpendicular to AE at K.
Prove that:
a) \u0394BHD \u2245 \u0394CKE (Triangle BHD is congruent to triangle CKE)
b) \u0394AHB \u2245 \u0394AKC (Triangle AHB is congruent to triangle AKC)<\/p>\n\n\n\n

Explanation<\/strong><\/p>\n\n\n\n

The provided image contains a handwritten geometry problem in Vietnamese. The transcription process involved a careful, step by step analysis of the script, guided by an understanding of common mathematical terminology and problem structures used in Vietnamese education.<\/p>\n\n\n\n

The text begins with “B\u00e0i 6,” which translates to “Problem 6.” The first sentence, “Cho \u0394ABC c\u00e2n t\u1ea1i A,” sets up the initial condition: “Given an isosceles triangle ABC with vertex A.” The following lines describe geometric constructions. The phrase “Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia BC l\u1ea5y \u0111i\u1ec3m D, tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia CB l\u1ea5y \u0111i\u1ec3m E” means “On the ray opposite to ray BC, take point D, and on the ray opposite to ray CB, take point E.” This is followed by the specific condition “sao cho BD = CE,” which means “such that BD = CE.”<\/p>\n\n\n\n

The next instruction, “K\u1ebb BH \u22a5 AD t\u1ea1i H. K\u1ebb CK \u22a5 AE t\u1ea1i K,” translates to “Draw BH perpendicular to AD at H. Draw CK perpendicular to AE at K.” The abbreviation “CMR” is a common shorthand for “Ch\u1ee9ng minh r\u1eb1ng,” the imperative to “Prove that.”<\/p>\n\n\n\n

The final two lines list the required proofs. The handwriting here is particularly challenging. However, recognizing the context of a geometry proof allows for accurate interpretation. What might initially appear as jumbled letters like “AISHQ” and “OCKE” are correctly identified as the notation for triangle congruence, “\u0394BHD = \u0394CKE.” Similarly, the second part is deciphered as “\u0394AHB = \u0394AKC.” This contextual interpretation is key, as these congruences represent a logical progression in solving this type of geometry problem, lending high confidence to the accuracy of the transcription despite the difficult script.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The Correct Answer and Explanation is: Correct Answer Here is the transcription of the handwritten Vietnamese text: B\u00e0i 6: Cho \u0394ABC c\u00e2n t\u1ea1i A.Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia BC l\u1ea5y \u0111i\u1ec3m D, tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia CB l\u1ea5y \u0111i\u1ec3m E sao cho BD = CE.K\u1ebb BH \u22a5 AD t\u1ea1i H. K\u1ebb CK \u22a5 AE t\u1ea1i […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-275404","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275404","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=275404"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275404\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=275404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=275404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=275404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}