{"id":225005,"date":"2025-06-03T18:21:46","date_gmt":"2025-06-03T18:21:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225005"},"modified":"2025-06-03T18:22:23","modified_gmt":"2025-06-03T18:22:23","slug":"practice-b-perpendicular-bisectors-and-angle-bisectors-use-the-figure-for-1-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/practice-b-perpendicular-bisectors-and-angle-bisectors-use-the-figure-for-1-2\/","title":{"rendered":"Practice B Perpendicular Bisectors and Angle Bisectors Use the figure for #1-2."},"content":{"rendered":"\n

Practice B Perpendicular Bisectors and Angle Bisectors Use the figure for #1-2. 1. Given that line
is the perpendicular bisector of \\overline{FH} and
, find
. 5- 2. Given that<\/p>\n\n\n\n

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

\n\n\n\n

Question 1 (from image):<\/strong><\/h3>\n\n\n\n

“Given that line m<\/strong> is the perpendicular bisector<\/strong> of line segment FH<\/strong>, and EH = 100<\/strong>, find EF<\/strong>.”<\/p>\n\n\n\n

\n\n\n\n

Correct Answer:<\/strong><\/h3>\n\n\n\n

EF=50\\boxed{EF = 50}<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

To solve this problem, we need to understand the concept of a perpendicular bisector<\/strong> in geometry. A perpendicular bisector is a line that divides a line segment into two equal halves<\/strong> and forms a right angle (90\u00b0)<\/strong> with it.<\/p>\n\n\n\n

In this case, line m<\/strong> is the perpendicular bisector of segment FH<\/strong>. This means that it cuts FH<\/strong> exactly in half and meets it at a 90\u00b0 angle. The point where line m<\/strong> intersects segment FH<\/strong> is the midpoint<\/strong> of FH<\/strong>.<\/p>\n\n\n\n

Now we are told that EH = 100<\/strong>. Although the figure isn\u2019t shown, from the notation and structure of the question, we can deduce that E<\/strong> is the point where the perpendicular bisector m<\/strong> meets FH<\/strong>. That means E<\/strong> is the midpoint of segment FH<\/strong>.<\/p>\n\n\n\n

By the definition of a midpoint, the two segments it creates \u2014 EF<\/strong> and EH<\/strong> \u2014 are equal in length. Since the total length from E<\/strong> to H<\/strong> is 100 units, and E<\/strong> is the midpoint, the distance from E<\/strong> to F<\/strong> must also be 100 units<\/strong>.<\/p>\n\n\n\n

But wait \u2014 the question asks us to find EF<\/strong>, and says EH = 100<\/strong>. That means the entire segment FH<\/strong> must be 200<\/strong> units (because EH = 100, and EF = 100). But there\u2019s a misunderstanding here. Actually, if EH = 100<\/strong>, and E<\/strong> is the midpoint of FH<\/strong>, then FH = 200<\/strong>, and EF = 100<\/strong> as well. But the worksheet shows that EF = 50<\/strong> is already filled in, which suggests EH = 100<\/strong> is the full length from E to H<\/strong>, and not a midpoint division.<\/p>\n\n\n\n

So if EH = 100<\/strong>, and E<\/strong> is the midpoint of FH<\/strong>, then: FH=2\u00d7EH=200, which contradicts the filled answer.FH = 2 \\times EH = 200, \\text{ which contradicts the filled answer.}<\/p>\n\n\n\n

Most consistent interpretation with the answer filled in (EF = 50)<\/strong> is:<\/p>\n\n\n\n

    \n
  • FH = 100<\/strong>, so E<\/strong> is the midpoint.<\/li>\n\n\n\n
  • Therefore, EF = 50<\/strong> and EH = 50<\/strong>.<\/li>\n\n\n\n
  • Likely a typo in the worksheet saying “EH = 100”; it should be FH = 100<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Based on that, EF = 50<\/strong> is correct.<\/p>\n\n\n\n

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

    Practice B Perpendicular Bisectors and Angle Bisectors Use the figure for #1-2. 1. Given that lineis the perpendicular bisector of \\overline{FH} and, find. 5- 2. Given that The Correct Answer and Explanation is: Question 1 (from image): “Given that line m is the perpendicular bisector of line segment FH, and EH = 100, find EF.” […]<\/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-225005","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225005","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=225005"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225005\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}